Coincidence Counting With NAI Scintillation Detectors

Coincidence Counting With NAI Scintillation Detectors ABSTRACT Coincidence counting is a technique employed in nuclear medicine for PET imaging. This technique utilizes a positron emitting radionuclide that is injected into patients to track biochemical and physiological processes. The positron annihilates with an electron and emit two 0.511MeV gamma rays which are detected simultaneously by two scintillation detectors. In the experiment, two gamma ray sources, 60Co and 22Na were used with a NaI scintillation counter. A single channel analyzer (SCA) was used to count the number of voltage pulses whose height fell within the gate width. The absolute efficiency and intrinsic efficiency was obtained as a function of distance. Real and random coincidences were determined from the spectrum obtained with varying gate width and gate delay for each source. The optimum gate width obtained was 5 µsec for both sources with gate delays of 1.2 µsec and 0.2 µsec for 22Na and 60Co respectively. The real coincidences for 22Na and 60Co were found to be 200 .1  ± 2.3 and 76.5  ± 1.7 respectively. The random coincidences obtained were 25.1  ± 3.4 and 13.4  ± 2.6 for 22Na and 60Co respectively. This was determined by using the LINEST function. The percentage thus of random to real coincidences obtained in this experiment was 12.54  ± 1.85 % and 17.52  ± 3.81 % for 22Na and 60Co respectively. It was deduced that the uncertainty in determining a random coincidence was higher in 60Co than in 22Na. the magnitude of the uncertainty is as a result of fluctuations in the instrumentation. Hence the Na system is more efficient for coincidence counting and so it is useful in the PET system. INTRODUCTION Coincident counting is a radiological measuring technique that is utilised in the nuclear medicine in the PET scan whereby two photons emitted from an event are detected simultaneously by a ring of detectors. Sodium Fluoride (F18-NaF) is the positron-emitting radionuclide employed in PET for bone imaging [1]. Upon decay, the positron are emitted which travels for a short distance and under Compton’s scattering thereby loosing most of its energy. It then undergoes annihilation with an electron and emit two high energy 0.511MeV photons. The 0.511MeV photons are emitted 180 degrees apart and interact with the PET detector rings at opposite sites. [2] The detectors are made up of scintillation crystals coupled with photomultiplier tubes powered by a high voltage which produces a pulse with a height proportional to the gamma-ray energy. A SCA counts the number of voltage pulses whose height falls within a predetermined window of photon energies. Coincidence measurement is utilised when a single detector cannot produce all the information expected, as gamma rays are randomly produced, hence the need to set several detectors. Real coincidences occur when two photons are emitted in coincidence from the same annihilation event and are detected simultaneously within a certain time frame set by the gate width. Random coincidences occur when two photons emitted from different events are detected simultaneously within the time frame of the gate width. [3] The gate width determines the time window within which the simultaneous emission of the gammas are detected. The optimum gate width therefore will ensure that the maximum number of real coincidences are detected to minimise the events of random coincidences. In the ideal situation when the gate width is zero the real coincidences can be observed, and with an increase in gate width the random coincidences can be observed. In the PET scan, this will ensure efficiency of the coincidence system. The need for the gate delay is to enable the second pulse to be detected within the time frame of the gate width and this is usually a minute time frame. It takes into account the minute fluctuations that occur at time of pulses. By alternating the gate delay and gate width, the rate of coincidence can be determined. In this experiment the two sources used were 60Co and 22Na. 60Co emit two gamma rays upon beta decay at energies 1.3325Mev and 1.1732MeV with 60Ni daughter nuclide. The 22Na undergoes a beta decay and electron capture decay with the emission of a 1.275MeV gamma photons and two 0.511Mev upon interactions with the detector material. The positron from the beta decay of 22Na annihilates an electron of the detector and emit the two gammas at 0.511Mev energies at 1800. The coincidence counting system records just a certain portion of events depending on the solid angle as a function of distance. Coincidence counting as a function of distance is maximum in the middle and zero at the edge [4]. The photons can undergo several interactions in the detector before they are detected and that render the detector inefficient and so there is the need for its efficiency to be determined. The efficiency can be classed into two as absolute and intrinsic efficiencies and they are defined as Absolute efficiency ÃŽ µabs = Number of pulses recorded [3] Number of radiation quanta emitted by source Intrinsic efficiency ÃŽ µint = Number of pulses recorded [3] Number of radiation quanta incident on detector These efficiencies are related by ÃŽ µint = ÃŽ µabs * (4à ¯Ã¢â€š ¬Ã¢â‚¬  /à ¢Ã¢â‚¬Å¾Ã‚ ¦) [3] where à ¢Ã¢â‚¬Å¾Ã‚ ¦ is the solid angle of the between source and detector. The solid angle is dependent on the distance between source and detector (d) and the radius of the detector (r) and it is determined by the this equation, à ¢Ã¢â‚¬Å¾Ã‚ ¦ = 2à ¯Ã¢â€š ¬Ã¢â‚¬   1 d [3] √d2 + r2 To determine the efficiency of the coincidence system, the absolute efficiency for real and random coincidences were also determined for both sources based on the equations below. ÃŽ µabs for real coincidences for 22Na = ÃŽ µabs * ÃŽ µint ÃŽ µabs for random coincidences for 22Na = (ÃŽ µabs)2 * Activity * Intensity * Time ÃŽ µabs for real coincidences for 60Co = ÃŽ µabs * ÃŽ µabs ÃŽ µabs for random coincidences for 60Co = (ÃŽ µabs)2 * Activity * Intensity * Time METHOD Two NaI detectors coupled with photomultipliers with high voltages and preamplifiers were used for this experiment. The inputs were connected to spectroscopic and SCA amplifiers. Detector 1 was first corrected for background by counting for 5 minutes. The 22Na gamma ray source was varied with distance and the absolute efficiency of the detector was determined as a result. Detector 2 was introduced and set at a distance of 10cm apart from Detector 1. 22Na was positioned in the middle and the counting was set to 5 minutes. The gate width and gate delay were varied and their spectrum observed. The experiment was repeated for the second gamma ray source, 60Co. The optimum gate delay was determined and varied with the gate width to obtain the optimum gate width. A linear graph of count rate against gate width was obtained that showed the real and random coincidences based on the slope gradient obtained. The percentage ratio of the random to real coincidences were determined and the uncertainty associated with the experiment was also determined. RESULTS/DISCUSSION The background spectrum was corrected in the count reading for both sources. The background radiation is as a result of scattered radiation associated with the experiment. The absolute efficiency of the detector was determined for both sources as shown in Figure 1 and Figure 2 and Table 1a 1b and Table 2a 2b for 22Na and 60Co respectively. The absolute efficiency was obtained using the formula Absolute efficiency = Sum of count Intensity x Activity Figure 1: Absolute efficiency as a function of the distance between the 22Na source and detector Figure 2: Absolute efficiency as a function of distance between the 60Co source and detector The 22Na revealed a gradual decrease in efficiency with increasing distance, whereas 60Co revealed a rapid drop in efficiency as a function of distance. 60Co revealed lower absolute efficiencies since the measure of the number of pulses obtained by the 60Co was less than the number of photons emitted by the gamma ray source. This could have been due to Compton scattering reducing the number of photons actually detected as a pulse. The 22Na however revealed quite high absolute efficiencies and so can be confirmed that the detector was efficient in detecting the 22Na than the 60Co. The intrinsic efficiency was determined using the equation below. ÃŽ µint = ÃŽ µabs * (4à ¯Ã¢â€š ¬Ã¢â‚¬  /à ¢Ã¢â‚¬Å¾Ã‚ ¦) The solid angle was determined for the detector when the distance between both detectors was varied between 5cm to 20cm and the radius of the detector was measured as 10cm. This is shown in Tables 3 and 4 and Figures 3 and 4 for 22Na and 60Co respectively. Figure 3: Intrinsic efficiency as a function of distance between the 22Na source and detector Figure 4: Intrinsic efficiency as a function of distance between the 60Co source and detector The intrinsic efficiency for 60Co was lower than 22Na. It can be deduced that the number of 60Co photons incident on the detector was more than the number of pulses recorded. Hence signifying that the detector was not efficient in detecting the 60Co. The 22Na however displayed high intrinsic efficiency almost approximating the maximum value for intrinsic efficiency. The intrinsic efficiency were found to be fluctuating with the highest being 0.9898 and 0.3872 with a solid angle of 1.3029 at 13cm distance from detector for 22Na and 60Co respectively. This is as result of the detector’s geometry detecting the photons at different solid angles. The solid angle determines how much of the photons can be detected as a function of distance. The overlap of the error bars signifies the uniformity of the errors. The probability of a 0.511MeV gamma travelling in the direction of the detector and being absorbed by it, will imply that the second 0.511MeV will also travel in the correct direction. Both detectors detecting the two 0.511MeV gammas can be determined to yield the absolute efficiency for real coincidences. This can be deduced from the notion that photons travelling in the right direction will be absorbed in the right direction by both detectors. The results of absolute efficiencies for real and random coincidences for 22Na and 60Co is shown in Table 5 6 and Figure 5, 6, 7 8. The efficiencies for both sources decreased with distance and it was lower for 60Co. The absolute efficiency for random coincidences was however for both sources than the absolute efficiency for real coincidences. It can thus be inferred that the absolute efficiencies for real coincidences for both 22Na and 60Co yields less probability of detection of real coincidence with 60Co as compared to the 22Na. The abso lute efficiencies for random coincidences was however comparable for both sources as the probability of detecting the second event within the gate width is possible for both sources. Figure 5: Absolute efficiency for real coincidences as a function of distance for 22Na Figure 6: Absolute efficiency for random coincidences as a function of distance for 22Na Figure 7: Absolute efficiency for real coincidences as a function of distance for 60Co Figure 8: Absolute efficiency for random coincidences as a function of distance for 60Co The gate delay was varied with gate width to obtain the optimum values of delay and width. The optimum gate delay was obtained as 1.2 µsec and 0.2 µsec for both 22Na and 60Co respectively and was used for the experiment. A linear graph of count rate as a function of gate width was obtained and a fixed gate width was obtained as shown in Figure 5 and 6 and table 7 and 8 Figure 5: A linear graph of count rate as a function of gate width applying a 1.2 µsec gate delay for 22Na Figure 6: A linear graph of count rate as a function of gate width by applying a 0.2 µsec gate delay for 60Co Real coincidences occur on the intercept of the linear slope gradient, whereas random coincidences can be found with the slope. For 22Na the optimum gate width obtained was 5 µsec. The graph of count rate as a function of gate width yielded a slope gradient of y = 5.019x + 200.15. By applying the optimum gate width and correcting for the gate delay, the real and random coincidences were determined using the LINEST function. The real coincidences was found to be 200  ± 2.3 whereas the random coincidences was found to be 25.1  ± 3.4. The percentage thus of random to real coincidences obtained in this experiment was 12.54  ± 1.85 %. This gives the value of pure coincidences that are not dependent on gate width. For 60Co, the optimum gate width was 5 µsec. The graph of count rate as a function of gate width yielded a slope gradient of y = 2.6801x + 76.483. When the optimum gate width was applied whilst correcting for the minute gate delay, the real and random coincidences were determined using the LINEST function. The real coincidences was found to be 76.5  ± 1.7 whereas the random coincidences was found to be 13.4  ± 2.6. The percentage of random to real coincidences obtained in this experiment was 17.52  ± 3.81 %. The above results was compared with the measured values obtained from the graph. The intercept gave the real coincidences as 200.15 and 76.48 for 22Na and 60Co respectively. The point of data convergence on the straight line gave the optimum gate width and the count equivalent was found as 225.28 and 90.02 for 22Na and 60Co respectively. The difference between this value and the real coincidences yielded the random coincidences as 25.13 and 13.56 in 22Na and 60Co respectively. Hence the percentage ratio of the random and real coincidences was obtained as 12.49% and 17.73%. This is equivalent to the values obtained from the calculated coincidences with the differences being due to uncertainties. The uncertainties with this experiment were with the NaI detector which contributed to scatter around the cover. The count rates resulted in some uncertainties as well and has been sown in table 8 for both detectors. The solid angle presented an uncertainty as the measurements for the detector could incur a large margin of errors. From all the results synthesized for both sources it could be gathered that the 22Na was an efficient source for coincidence counting compared to the 60Co. This is as a result of the geometry of the detectors as the Co system does not show a coincidence system and so there is more likelihood of a random coincidence than a real coincidence as compared to the Na system. This concludes that the 22Na will be efficient in a PET system, hence the reason for positron emitting radioisotopes being used in the PET system to ensure the maximum number of coincidences are being detected CONCLUSION The experiment was performed to examine the coincidence counting in two gamma ray sources and to determine the real and random coincidences as a function of gate width. The optimum gate width obtained was 5 µsec for both sources with gate delays of 1.2 µsec and 0.2 µsec for 22Na and 60Co respectively. The real coincidences for 22Na and 60Co were found to be 200.1  ± 2.3 and 76.5  ± 1.7 respectively. The random coincidences obtained were 25.1  ± 3.4 and 13.4  ± 2.6 for 22Na and 60Co respectively. This was determined by using the LINEST function. The measured count rates was also determined from the graph and resulted in real coincidences for 22Na and 60Co respectively as 200.15 and 76. 48 and random coincidences of 25.13 and 13.56. The percentage thus of random to real coincidences obtained in this experiment was 12.54  ± 1.85 % and 17.52  ± 3.81 % for 22Na and 60Co respectively. This gave the quality of the uncertainty in the coincidence system. It was deduced that the uncertainties in determining a random was higher in 60Co than in 22Na hence the Na system is more efficient for coincidence counting and very useful in the PET system. REFERENCES [1] The detection of bone metastases in patients with high-risk prostate cancer:99mTc-MDP planar bone scintigraphy, single- and multi-field-of-view SPECT,18F-fluoride PET, and18F-fluoride PET/CT.Even-Sapir et al, J Nucl Med(2006)47:287–97 [2] The Physics of Medical Imaging, ed. S. Webb. IoP publishing [3] Radiation and Detection Measurement, Glen N Knoll, 3rd Edition [4] Coincidence Counting, E. K. A. Advanced Physics Laboratory, Physics 3081, 4051 APPENDIXES Table 1a: Counts rate as a function of distance between source and detector for 22Na Table 1b: Absolute efficiency as a function of distance between source and detector for 22Na Table 2a: Counts rate as a function of distance between source and detector for 60Co Table 2b: Absolute efficiency as a function of distance between source and detector for 60Co Table 3: Intrinsic efficiency as a function of distance between source and detector of 22Na Table 4: Intrinsic efficiency as a function of distance between source and detector for 60Co Table 5: ÃŽ µabs for real and random coincidences as a function of distance for 22Na Distance(cm) ÃŽ µabs à ¢Ã¢â‚¬Å¾Ã‚ ¦ 4à ¯Ã¢â€š ¬Ã¢â‚¬   ÃŽ µint ÃŽ µabs for real coincidences ÃŽ µabs for random coincidences 5 0.09940 3.473 12.57 0.35967 0.0994 48.7255 10 0.05091 1.8403 12.57 0.347637 0.0509 12.8015 13 0.04015 1.3029

No Groove in the Gunsights by Lars Kullberg :: essays research papers

No Groove in the Gunsights Always under the thumb of his dark mistress, the speaker struggles beneath her power. Try as he may, he will never be able to break the tie of lust between the two. His threats are not threatening to her, and he knows this. His power is beneath her's, and he knows this as well. By threatening his lover in the 140th sonnet, the speaker is merely admitting to his own helplessness to which he is forever bound. This appears to be the first sonnet in which he is taking a stand. Never before has he spoken in such a threatening tone: "Be wise†¦do not press/My tongue tied patience†¦" (140. 1-2). One might think that he is now revealing for the first time his yet unheard of power. But he has no such power. He knows that his threats do not frighten her†¦ so why does he even bother? Sure, he could untie his tongue and let the world know of her habits. However, no one would care. She is a dark lady—she and others like her are meant to be that way. He would only be telling what is already known. However, what she has to tell of him is not already known. Being a married man, he is not expected to have a mistress. She is his only mistress. They both know this as well. If he were to lose her, he would have nothing left. She knows his lust for her—his need for her. She knows he lives for her darkness and for the pleasure he finds in her†¦ temporary as it may be. Temporary yet lasting. There may be times when he thinks he can live without her, but the time comes again soon when he feels the familiar lust again. It is the lack of love which makes it temporary. However, it is the abundance of lust which makes it permanent. He is only one of her many lovers. If she were to loose him, she would still have many others to satisfy her. She takes comfort in the fact that he needs her and he remains under her thumb to almost any extent. The speaker knows she has many lovers. He claims to hate her unfaithfulness, but in fact he likes it. He likes the fact that she is nothing more than an object of sex†¦of temporary pleasure. If she were really in love with him and were truly faithful, he would be less attracted to her. The passion and the lust would be gone. So the question remains—why does he bother with these empty threats?

Historical Development of Labour Law

The origins of labour law can be traced back to the remote past and the most varied parts of the world. While European writers often attach importance to the guilds and apprenticeship systems of the medieval world, some Asian scholars have identified labour standards as far back as the Laws of Hammurabi and rules for labour–management relations in the Laws of Manu; Latin-American authors point to the Laws of the Indies promulgated by Spain in the 17th century for its New World territories. None of these can be regarded as more than anticipations, with only limited influence on subsequent developments. Labour law as it is known today is essentially the child of successive industrial revolutions from the 18th century onward. It became necessary when customary restraints and the intimacy of employment relationships in small communities ceased to provide adequate protection against the abuses incidental to new forms of mining and manufacture on a rapidly increasing scale at precisely the time when the 18th-century Enlightenment, the French Revolution, and the political forces that they set in motion were creating the elements of the modern social conscience. It developed rather slowly, chiefly in the more industrialized countries of western Europe, during the 19th century and has attained its present importance, relative maturity, and worldwide acceptance only during the 20th century. The first landmark of modern labour law was the British Health and Morals of Apprentices Act of 1802, sponsored by the elder Sir Robert Peel. Similar legislation for the protection of the young was adopted in Zurich in 1815 and in France in 1841. By 1848 the first legal limitation of the working hours of adults was adopted by the Landsgemeinde (citizens’ assembly) of the Swiss canton of Glarus. Sickness insurance and workmen’s compensation were pioneered by Germany in 1883 and 1884, and compulsory arbitration in industrial disputes was introduced in New Zealand in the 1890s. The progress of labour legislation outside western Europe, Australia, and New Zealand was slow until after World War I. The more industrialized states of the United States began to enact such legislation toward the end of the 19th century, but the bulk of the present labour legislation of the United States was not adopted until after the Depression of the 1930s. There was virtually no labour legislation in Russia prior to the October Revolution of 1917. In India children between the ages of seven and 12 were limited to nine hours of work per day in 1881 and adult males in textile mills to 10 hours per day in 1911, but the first major advance was the amendment of the Factory Act in 1922 to give effect to conventions adopted at the first session of the International Labour Conference at Washington, D. C. , in 1919. In Japan rudimentary regulations on work in mines were introduced in 1890, but a proposed factory act was controversial for 30 years before it was adopted in 1911, and the decisive step was the revision of this act in 1923 to give effect to the Washington Convention on hours of work in industry. Labour legislation in Latin America began in Argentina in the early years of the century and received a powerful impetus from the Mexican Revolution, which ended in 1917, but, as in North America, the trend became general only with the impact of the Great Depression. In Africa the progress of labour legislation became significant only from the 1940s onward. The legal recognition of the right of association for trade union purposes has a distinctive history. There is no other aspect of labour law in which successive phases of progress and regression have been more decisively influenced by political changes and considerations. The legal prohibition of such association was repealed in the United Kingdom in 1824 and in France in 1884; there have been many subsequent changes in the law and may well be further changes, but these have related to matters of detail rather than to fundamental principles. In the United States freedom of association for trade union purposes remained precarious and subject to the unpredictable scope of the labour injunction, by means of which the courts helped restrain trade union activity until the 1930s. The breakthrough for trade unionism and collective bargaining was achieved by the National Labor Relations Act of 1935. In many other countries the record of progress and regression with respect to freedom of association falls into clearly distinguished periods separated by decisive political changes. This has certainly been the case with Germany, Italy, Spain, Japan, and much of eastern Europe; there have been many illustrations of it, and there may well be more in the developing world. Labour codes or other forms of comprehensive labour legislation and inistries of labour were not introduced until the 20th century. The first labour code (which, like many of its successors, was a consolidation rather than a codification) was projected in France in 1901 and promulgated in stages from 1910 to 1927. Among the more advanced formulations affecting the general condition of labour were the Mexican Constitution of 1917 and the Weimar Constitution of Germany of 1919, both of which gave constitutional status to certain general principles of social policy regarding economic rights. Provisions of this kind have become increasingly common and are now widespread in all parts of the world. Departments or ministries of labour responsible for the effective administration of labour legislation and for promoting its future development were established in Canada in 1900, in France in 1906, in the United States in 1913, in the United Kingdom in 1916, and in Germany in 1918. They became general in Europe and were established in India and Japan during the following years and became common in Latin America in the ’30s. A labour office was established in Egypt in 1930, but only in the ’40s and ’50s did similar arrangements begin to take root elsewhere in Asia and Africa. Under differing political circumstances there continue, of course, to be wide variations in the authority and effectiveness of such administrative machinery.

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