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Experimental determination of the extrinsic sensitivity and counting efficiency of a nuclear gamma camera using a homogeneous circular planar source
ARTICLE IN PRESS
Applied Radiation and Isotopes 65 (2007) 114–119 www.elsevier.com/locate/apradiso
Experimental determination of the extrinsic sensitivity and counting efficiency of a nuclear gamma camera using a homogeneous circular planar source Matthew Rodrigues, Eduardo Galiano Department of Physics, Laurentian University, Ramsey Lake Road, Sudbury, Ont., Canada P3E 2C6 Received 16 February 2006; accepted 27 June 2006
Abstract Two important operational parameters of medical gamma cameras are the extrinsic counting efficiency and sensitivity. Historically, for practical reasons these two parameters have been defined using a point source of radiation at a certain distance from the detector. This definition has the disadvantage of producing measurements of limited clinical relevance since real patients are not point sources of radiation. In this work, we propose a more clinically relevant method of determining efficiency and sensitivity, using a planar, circular, homogeneous source. For this purpose, a gamma camera of 39 cm diameter, and a circular, homogeneous, 36.5 cm diameter Co-57 source with an activity of 5.570.7% mCi were employed. The source was placed coaxially with the detector at distances of 50, 100, and 150 cm. Data were acquired using a medium and a high-resolution collimator. The efficiency was found to depend directly on the solid angle subtended by the detector. Computed values for the sensitivity are in the range of 5–6 kcts/sec-mCi, and values for the efficiency were found to range between 0.2% and 2%. The results show an approximate 2:1 ratio in sensitivity and efficiency between the medium and high-resolution collimators regardless of source–detector distances. r 2006 Elsevier Ltd. All rights reserved. Keywords: Gamma camera; Coaxial source detector system; Solid angle; Extrinsic sensitivity; Extrinsic counting efficiency
1. Introduction Two important operational parameters of all medical nuclear gamma cameras are the extrinsic counting efficiency and the extrinsic sensitivity. Historically speaking, these two parameters have always been specified by equipment manufacturers and clinical users by employing a point-like source of radiation at a certain distance from the detector (Rollo, 1977; Sprawls, 1981; Early et al., 1995). This is a convenient way of defining the parameters, as it greatly facilitates the techniques required to carry out the physical measurements involved. However, the definitions in their present form have the disadvantage of providing measurements which are of limited clinical relevance since it is well known that patients do not behave as point-like Corresponding author. Tel.: +1 705 675 1151; fax: +1 705 673 4868.
E-mail address: [email protected] (E. Galiano). 0969-8043/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2006.06.003
sources of radiation. In fact, patients behave as large, distributed sources of radiation. In this work, we propose the introduction of a more clinically relevant method of determining efficiency and sensitivity, by replacing the point source with a planar, circular, homogeneous source. No reports have been found in the literature of such a proposal. When attempting to quantify the counting efficiency and sensitivity of medical nuclear equipment containing circular alkyl halide scintillators, the problem can be modeled as a coaxial source–detector system. A difficulty with this approach has been the determination of the solid angle subtended by the source with respect to the detector. The problem in fact has implications in fields other than nuclear medicine, such as a spectroscopy (Profio, 1976; Knoll, 2000; Johansson et al., 2003). In the nuclear industry, Holcomb et al. (1967) used the known solutions of the problem in their time in order to solve a complex
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
theoretical issue related to waste disposal. Das and Kenny (1995) have rediscovered the problem when assaying brachytherapy sources with a special miniature circular ion chamber. The geometry in Fig. 1 depicts a circular homogeneous radiation source of diameter ‘x’ placed at a distance ‘d’ from a circular detector of diameter ‘r’. Segre (1959) has published an equation that directly relates these three parameters to the solid angle. This equation was modified and solved in closed form by Knoll (2000) by setting x ¼ 0 i.e., the case of a point source. Ruby (1995) proposed an integral of Bessel functions as a solution to the problem and followed this with a closed-form approximation of that equation. The history of the problem has seen other noteworthy approximations over the last halfcentury, going all the way back to an expression by Burtt (1949). In 1983, Tsoulfanidis published a solution to Ruby’s integral expression (Tsoulfanidis, 1983). Pomme´ (2004) offered a complete series expansion of Ruby’s integral equation, and more recently, Aguiar and Galiano (2004) have derived an expression that incorporates elements from both Segre’s and Ruby’s equations. In a recent investigation, it has been determined that the equations by Segre, Knoll, and Ruby show the best degree of self-correlation and the best agreement with benchmark Monte Carlo calculations. In the same study, it was concluded that the equations by Burtt, Tsoulfanidis, Pomme´, and Aguiar and Galiano do not perform as well, and thus would not be suitable for experimental purposes (Galiano and Rodrigues, 2006). In nuclear counting equipment, a certain amount of time must separate two events in order for them to be recorded as two separate pulses by the electronics. This time separation has been referred to as the ‘dead time’ since during this time, no event occurring in the detector will be
115
registered. There are two ways to model this phenomenon: either as non-paralyzable or as paralyzable. The nonparalyzable model involves a fixed value of dead time while in the paralyzable model, the dead time can be renewed with each new event occurring in the detector (Knoll, 2000). When dealing with Anger scintillation cameras in particular, this latter form of machine paralysis can cause significant count losses at high count rates and has been determined to exist in the camera-processing unit used in this work, specifically in the analog-to-digital converters (Glass and Vernon, 1972). A second issue that presents itself at high count rates is known as pile-up. The pulses from radiation detectors are randomly spaced and thus when the count rates are high, interfering effects between pulses cause distortions. As with paralysis, there are two types of pile-up. The first is known as tail pile-up which involves a superposition of pulses in the long duration tail, or undershoot, of a preceding pulse. The second type is known as peak pile-up. This occurs when two pulses are so close together that the processor treats them as one single pulse (Knoll, 2000). In this work, the extrinsic counting efficiency and extrinsic sensitivity of an Anger-type scintillation nuclear camera are determined using a flat circular homogeneous Co-57 source of 36.5 cm and an activity of 5.570.7% mCi. These parameters have been determined using a medium and a high-resolution collimator at source–detector distances of 50, 100, and 150 cm.
2. Materials and methods In a previous study, three equations were found to exhibit acceptable accuracy and reasonable self-correlation when determining the solid angle subtended by a circular detector for a coaxial homogeneous circular source (Galiano and Rodrigues, 2006). The first of these was published by Segre (1959) ( " #) 3 x2 2y0 2 O1 ¼ 4p 1 cos y0 1 þ , (1) sin 2 d2 4 where y0 ¼ arctan
r . 2d
Knoll (2000) obtained a simplified version of Eq. (1) by setting x ¼ 0, i.e., a point source O2 ¼ 4pf1 cosðy0 Þg.
(2)
Ruby (1994) presented the problem as an integral of Bessel functions of the following form: O¼ Fig. 1. Geometrical arrangement of the coaxial source–detector assembly.
Rd Rs
Z 0
1
k1 ekd J 1 ðkRs ÞJ 1 ðkRd Þ dk
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
116
for which he obtained the following closed-form approximation as a solution
r2 3 x2 r 2 O3 ¼ 4p þ 1 4 d 2d 8d 2 x2 r 2 5 x 4 r 4 þ þ þ3 8 d 2d d 2d x2 r 2 35 x 6 r 6 þ þ6 64 d 2d d 2d 2 2 x r þ . d 2d
ð3Þ
A clinical nuclear camera (Elscint APEX SP-4, Israel) containing a NaI(Tl) detector crystal of approximately 39 cm in diameter and a 36.5 cm diameter Co-57 source (GE Healthcare model CTRF 10051, Mississauga, ON, Canada) at source–detector distances of 50, 100, and 150 cm were used for this investigation. The solid angle subtended by the detector was computed using the three equations above. It has previously been determined that the average value of Eqs. (1)–(3), OAv123, is adequate to describe the solid angle C and thus, these values have been used for calculations (Galiano and Rodrigues, 2006). A parallelepiped support was constructed out of wood in order to suspend the Co-57 source at the various distances ‘d’ above the detector head
as seen in Fig. 2. A simple plumb bob composed of string and a tiny weight was used to ensure that the source was centered directly over the camera’s detector head. The camera was programed to record five million counts of the 122 keV photons emitted from the Co-57 source with a 710% energy window. Collecting more than five million counts did not significantly improve the image quality. A medium and a high-resolution collimator were used separately to image the source at each height d. These parallel-hole collimators contain lead septa that in effect, attempt to resolve the source by attenuating non-perpendicular photons that are incident on the detector head. Although the exact dimensions of individual septa in the collimators are unknown, there is a clear difference seen in the results between the high-resolution and mediumresolution collimators. These differences are analyzed in Section 3. The time and count rate of each individual image acquisition can be found in Table 1. The extrinsic counting efficiency e is defined as the number of counts ‘N’ recorded by the detector in a certain time interval ‘t’, divided by the number of counts ‘NTH’ that theoretically strike the detector surface in that same time interval, with a collimator in place. To determine e, the geometric efficiency G defined as C/4p, had to be computed (Galiano and Rodrigues, 2006). We also require that the activity ‘A’ of the source be known, which for this work was 5.5 mCi70.7%. Finally, the gamma photon emission probability ‘F’ for the decay of Co-57 is 85.6%. Using these parameters, the extrinsic counting efficiency for 122 keV photons for a distributed source is given by ¼
N N4p . ¼ N TH CFAt
(4)
The extrinsic sensitivity ‘s’, is defined as the count rate per unit source activity at a certain distance, also with the
Table 1 The source–detector distance, collimator used, total counts recorded, total acquisition times, and count rates Distance of source from detector (cm)
Collimator used
Total number of counts recorded
Acquisition time (s)
Count rate (counts/s)
50
Medium resolution High resolution
5 106
153
32,680
327
15,291
Medium resolution High resolution
170
29,412
372
13,441
Medium resolution High resolution
178
28,090
397
12,594
100
150 Fig. 2. Experimental setup used where ‘x’ is the source diameter, ‘r’ is the detector diameter, and ‘d’ is the source–detector distance.
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
collimator in place. In mathematical terms N . (5) At The parameters used in Eqs. (4) and (5) are not absolute and therefore have inherent uncertainties. The uncertainty in N, sN, was experimentally determined to be 712000 since this value was the approximate minimum number of counts recorded per second when acquiring data, as seen in Table 1. The uncertainty in time st was 70.5 s. The manufacturer of the Co-57 source has quoted an uncertainty in the source activity of 0.7%. Finally, the uncertainty in the solid angle C was determined to be a ratio of half of the smallest unit of measure divided by the total diameter of the detector head. This gives sC ¼ 7(0.5 cm/39.0 cm) ¼ 70.0128 steradians.
s¼
117
source–detector distance. This was in fact observed, as seen in Table 2. For example, as the source-detector distance increases from 50 to 100 cm and then to 150 cm, the sensitivity decreases from 5941 to 5347 counts/s-mCi, and to 5107 counts/s-mCi, respectively, for the medium-resolution collimator. This result is rather simple to predict if one considers that the solid angle decreases with distance. This causes the theoretical number of photons striking the detector surface to decrease, and therefore causes the number of photons actually counted to also decrease. The average uncertainty in the sensitivity of this collimator was determined to be approximately 724 counts/s-mCi, which is less than 1% of the measured sensitivity at any of the three distances. The same general trends are verified for the high-resolution collimator. Fig. 3 shows a graphical
3. Results and discussion Table 1 contains acquired data and Table 2 contains calculated values for the extrinsic counting efficiency and extrinsic sensitivity, as well as their associated uncertainties. Examining Table 1, as the source–detector distance increases from 50 cm, through 100 cm, and then to 150 cm, the acquisition time increased from 153 to 170 s, and then 173 s, respectively, for the medium-resolution collimator. This is not unexpected since the value for the solid angle decreases from 0.6454 to 0.2181 steradians and to 0.1019 steradians, respectively. This decrease in the average solid angle is responsible for the decrease in the counting rate as the source–detector distance is increased. These trends are observed for both the medium and high resolution collimator and a ratio of approximately 2:1 is apparent between the two collimators for the acquisition time as well as the count rate. Since the count rate varies inversely with source–detector distance, one would expect from Eq. (5) that the sensitivity would also decrease with an increase in
Fig. 3. Extrinsic sensitivity versus source–detector distance for both medium and high-resolution collimators. Values for the medium-resolution collimator are approximately twice those of the high-resolution collimator.
Table 2 The source–detector distance, collimator used, average solid angle, extrinsic counting efficiency and extrinsic sensitivity and their corresponding uncertainties Source–detector distance (cm)
Collimator used
Average solid angle (steradians)
Extrinsic counting efficiency (%)
Uncertainty in extrinsic counting efficiency (7%)
Extrinsic sensitivity (counts/s/mCi)
Uncertainty in extrinsic sensitivity (7counts/s-mCi)
50
Medium resolution High resolution
0.6454
0.365
7.394 105
5941.771
25.273
0.17
3.424 105
2780.095
20.855
Medium resolution High resolution
0.2181
0.972
5.723 104
5347.594
24.272
0.445
2.613 104
2443.793
20.541
Medium resolution High resolution
0.1019
1.989
2.500 103
5107.252
23.887
0.891
1.121 103
2289.902
20.409
100
150
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M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
representation of the approximate 2:1 sensitivity ratio between the medium and high-resolution collimators. For the medium-resolution collimator, as the source–detector distance increases from 50 to 100 cm then to 150 cm, the counting efficiency increases from 0.365% to 0.972% then to 1.989%. The average uncertainty was calculated to be 71.049 103%, again within 1% of the measured values. The high-resolution collimator follows the same general trend. In the case of the high-resolution collimator, the average uncertainty was approximately 74.722 104%, also within 1% of the measured values. Fig. 4 shows the efficiency trends for the medium and high-resolution collimators. In principle, the extrinsic counting efficiency should be independent of source-to-detector distance. To further investigate our apparently contradictory results for efficiency, the experimental setup was altered in two ways. First, the Co-57 source was placed directly on top of the collimator, i.e., a d ¼ 0 situation. Second, the collimator was removed from the detector head and the source was placed at d ¼ 50 cm. In both cases, the camera registered approximately five counts in the first few seconds of acquisition. As the acquisition time continued, the number of counts did not increase by any significant amount, and the acquisition was stopped. These results have led us to believe that machine paralysis, specifically a paralyzable model, is occurring in our camera and may partially explain our results (Knoll, 2000). Each time a gamma photon interacts with the detector crystal, a certain amount of time is needed for the camera’s electronics to record that interaction and display it on the image screen. Since the camera’s electronics are insensitive to any photon interaction during this fixed period, this time has been labeled the dead time (t). In paralyzable dead time, any interactions that take place in the fixed period t will extend the dead time by another period t. The actual value of t is not
known for the camera used in this investigation, but modification of the setup has shown that it is clearly long enough to be affected by count rates that are of the order of 104 counts/s. The problem of somehow accounting for dead time losses has received considerable attention in the past. Glass and Vernon (1972) developed a method based on a technique described by Anders (1969) that modifies the electronics of the camera in order to estimate the total counting losses that occur in the system. Madsen and Nickles (1986) were able to correct count-rate losses by comparing the ratio of the count rate from a reference source to data from the reference source fitted to a paralyzable model of dead time. Adams and Mena (1988) used an algorithm and two Fortran programs to accurately determine the dead time of a scintillation camera using a short-lived radionuclide and multiple copper filters. Recently, Mowlavi et al. (2006) developed a Monte Carlo code using Fortran PowerStation 4.0 software to correct pile-up distortion in gamma camera spectroscopy. This Monte Carlo code demonstrated that the Siemens e.Cam gamma camera acts as a paralyzable system in high true count rate, rather than as a non-paralyzable system. This code can also be used with other cameras that have different counting systems in order to correct pile-up. In our work, we have made no systematic effort to compensate for dead time losses. 4. Conclusions The experimental feasibility of measuring the extrinsic counting efficiency and sensitivity of a nuclear medical gamma camera with a large source has been demonstrated. The results show that the sensitivity more or less follows a general inverse square relationship with respect to source–detector distance as expected from simple geometrical considerations. However, the extrinsic counting efficiency increased with an increase in source–detector distance—an unexpected result that we attribute to dead time effects. It is apparent that even at large source–detector distances, the phenomenon of dead time becomes a significant factor at high count rates i.e., in the order of 104 counts/s. Furthermore, the results show an approximate 2:1 ratio in both sensitivity and efficiency between the medium and high-resolution collimators. References
Fig. 4. Extrinsic efficiency versus source–detector distance for both medium and high-resolution collimators. The same approximate 2:1 ratio between collimators seen in the sensitivity (Fig. 3) holds for the efficiency.
Adams, A., Mena, R., 1988. Testing the count rate performance of the scintillation camera by exponential attenuation: decaying source; multiple filters. Med. Phys. 15 (3), 415–419. Aguiar, J.C., Galiano, E., 2004. Theoretical estimates of the solid angle subtended by a dual diaphragm–detector assembly for alpha sources. Appl. Radiat. Isot. 61, 1349–1351. Anders, O.U., 1969. Experiences with the Ge(Li) detector for highresolution gamma ray spectrometry and a practical approach to the pulse pileup problem. Nucl. Instrum. Meth. 68, 205–208. Burtt, B.J., 1949. Absolute beta counting. Nucleonics 5, 28. Das, K.R., Kenny, M.B., 1995. A thin parallel plate ionization chamber for calibration of microselectron sources. Radiother Onof. 37, 10–14.
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119 Early, P.J., Bruce, D., Sodee, M.D., 1995. Principles and Practice of Nuclear Medicine, second ed. C.V. Mosby. Galiano, E., Rodrigues, M., 2006. A comparison of different analytical methods of determining the solid angle of a circular co-axial sourcedetector system. Appl. Radint. Isot. 64, 497–501. Glass, H.I., Vernon, P., 1972. A method of correcting for count rate losses in dynamic gamma camera studies. Phys. Med. Biol. 17 (6), 843–845. Holcomb, W.F., Paige, D.M., Stevenson, C.E., Graham, D.E., 1967. High level radioactive solid waste burial operations for the EBR-II fuel cycle facility. Nucl. Eng. Des. 5, 221–227. Johansson, L., Altzitzoglou, T., Sibbens, G., Pomme, S., Denecke, B., 2003. Standardization of 238Pu using four methods of measurement. Nucl. Instrum. Meth. A. 505, 699–706. Knoll, G.F., 2000. Radiation Detection and Measurement, third ed. Wiley, New York, pp. 116–118. Madsen, M.T., Nickles, R.J., 1986. A precise method for correcting countrate losses in scintillation cameras. Med. Phys. 13 (3), 344–349.
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Mowlavi, A.A., Denardo, M., Fornasier, M.R., Binesh, A., 2006. Monte Carlo simulation of intrinsic count rate performance of a scintillation camera for diagnostic images. Appl. Radiat. Isot. 64, 390–395. Pomme´, S., 2004. A complete series expansion of Ruby’s solid angle formula. Nucl. Instrum Meth. A 531, 616–620. Profio, A.E., 1976. Experimental Reactor Physics. Wiley, New York, pp. 137–138. Rollo, F.D., 1977. Nuclear Medicine Physics and Agents. C.V. Mosby Co. Ruby, L., 1995. Further comments on the geometrical efficiency of a parallel disk-source and detector system. Nucl. Instrum Meth. A. 337, 531–533. Segre, E., 1959. Experimental Nuclear Physics, vol. 3. n cmcm, pp. 435–438. Sprawls, P., 1981. The Physics and Instrumentation of Nuclear Medicine. University Park Press. Tsoulfanidis, N., 1983. The defined solid angle method. In: Measurement and Detection of Radiation. Hemisphere Publishers Inc.
Applied Radiation and Isotopes 65 (2007) 114–119 www.elsevier.com/locate/apradiso
Experimental determination of the extrinsic sensitivity and counting efficiency of a nuclear gamma camera using a homogeneous circular planar source Matthew Rodrigues, Eduardo Galiano Department of Physics, Laurentian University, Ramsey Lake Road, Sudbury, Ont., Canada P3E 2C6 Received 16 February 2006; accepted 27 June 2006
Abstract Two important operational parameters of medical gamma cameras are the extrinsic counting efficiency and sensitivity. Historically, for practical reasons these two parameters have been defined using a point source of radiation at a certain distance from the detector. This definition has the disadvantage of producing measurements of limited clinical relevance since real patients are not point sources of radiation. In this work, we propose a more clinically relevant method of determining efficiency and sensitivity, using a planar, circular, homogeneous source. For this purpose, a gamma camera of 39 cm diameter, and a circular, homogeneous, 36.5 cm diameter Co-57 source with an activity of 5.570.7% mCi were employed. The source was placed coaxially with the detector at distances of 50, 100, and 150 cm. Data were acquired using a medium and a high-resolution collimator. The efficiency was found to depend directly on the solid angle subtended by the detector. Computed values for the sensitivity are in the range of 5–6 kcts/sec-mCi, and values for the efficiency were found to range between 0.2% and 2%. The results show an approximate 2:1 ratio in sensitivity and efficiency between the medium and high-resolution collimators regardless of source–detector distances. r 2006 Elsevier Ltd. All rights reserved. Keywords: Gamma camera; Coaxial source detector system; Solid angle; Extrinsic sensitivity; Extrinsic counting efficiency
1. Introduction Two important operational parameters of all medical nuclear gamma cameras are the extrinsic counting efficiency and the extrinsic sensitivity. Historically speaking, these two parameters have always been specified by equipment manufacturers and clinical users by employing a point-like source of radiation at a certain distance from the detector (Rollo, 1977; Sprawls, 1981; Early et al., 1995). This is a convenient way of defining the parameters, as it greatly facilitates the techniques required to carry out the physical measurements involved. However, the definitions in their present form have the disadvantage of providing measurements which are of limited clinical relevance since it is well known that patients do not behave as point-like Corresponding author. Tel.: +1 705 675 1151; fax: +1 705 673 4868.
E-mail address: [email protected] (E. Galiano). 0969-8043/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2006.06.003
sources of radiation. In fact, patients behave as large, distributed sources of radiation. In this work, we propose the introduction of a more clinically relevant method of determining efficiency and sensitivity, by replacing the point source with a planar, circular, homogeneous source. No reports have been found in the literature of such a proposal. When attempting to quantify the counting efficiency and sensitivity of medical nuclear equipment containing circular alkyl halide scintillators, the problem can be modeled as a coaxial source–detector system. A difficulty with this approach has been the determination of the solid angle subtended by the source with respect to the detector. The problem in fact has implications in fields other than nuclear medicine, such as a spectroscopy (Profio, 1976; Knoll, 2000; Johansson et al., 2003). In the nuclear industry, Holcomb et al. (1967) used the known solutions of the problem in their time in order to solve a complex
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
theoretical issue related to waste disposal. Das and Kenny (1995) have rediscovered the problem when assaying brachytherapy sources with a special miniature circular ion chamber. The geometry in Fig. 1 depicts a circular homogeneous radiation source of diameter ‘x’ placed at a distance ‘d’ from a circular detector of diameter ‘r’. Segre (1959) has published an equation that directly relates these three parameters to the solid angle. This equation was modified and solved in closed form by Knoll (2000) by setting x ¼ 0 i.e., the case of a point source. Ruby (1995) proposed an integral of Bessel functions as a solution to the problem and followed this with a closed-form approximation of that equation. The history of the problem has seen other noteworthy approximations over the last halfcentury, going all the way back to an expression by Burtt (1949). In 1983, Tsoulfanidis published a solution to Ruby’s integral expression (Tsoulfanidis, 1983). Pomme´ (2004) offered a complete series expansion of Ruby’s integral equation, and more recently, Aguiar and Galiano (2004) have derived an expression that incorporates elements from both Segre’s and Ruby’s equations. In a recent investigation, it has been determined that the equations by Segre, Knoll, and Ruby show the best degree of self-correlation and the best agreement with benchmark Monte Carlo calculations. In the same study, it was concluded that the equations by Burtt, Tsoulfanidis, Pomme´, and Aguiar and Galiano do not perform as well, and thus would not be suitable for experimental purposes (Galiano and Rodrigues, 2006). In nuclear counting equipment, a certain amount of time must separate two events in order for them to be recorded as two separate pulses by the electronics. This time separation has been referred to as the ‘dead time’ since during this time, no event occurring in the detector will be
115
registered. There are two ways to model this phenomenon: either as non-paralyzable or as paralyzable. The nonparalyzable model involves a fixed value of dead time while in the paralyzable model, the dead time can be renewed with each new event occurring in the detector (Knoll, 2000). When dealing with Anger scintillation cameras in particular, this latter form of machine paralysis can cause significant count losses at high count rates and has been determined to exist in the camera-processing unit used in this work, specifically in the analog-to-digital converters (Glass and Vernon, 1972). A second issue that presents itself at high count rates is known as pile-up. The pulses from radiation detectors are randomly spaced and thus when the count rates are high, interfering effects between pulses cause distortions. As with paralysis, there are two types of pile-up. The first is known as tail pile-up which involves a superposition of pulses in the long duration tail, or undershoot, of a preceding pulse. The second type is known as peak pile-up. This occurs when two pulses are so close together that the processor treats them as one single pulse (Knoll, 2000). In this work, the extrinsic counting efficiency and extrinsic sensitivity of an Anger-type scintillation nuclear camera are determined using a flat circular homogeneous Co-57 source of 36.5 cm and an activity of 5.570.7% mCi. These parameters have been determined using a medium and a high-resolution collimator at source–detector distances of 50, 100, and 150 cm.
2. Materials and methods In a previous study, three equations were found to exhibit acceptable accuracy and reasonable self-correlation when determining the solid angle subtended by a circular detector for a coaxial homogeneous circular source (Galiano and Rodrigues, 2006). The first of these was published by Segre (1959) ( " #) 3 x2 2y0 2 O1 ¼ 4p 1 cos y0 1 þ , (1) sin 2 d2 4 where y0 ¼ arctan
r . 2d
Knoll (2000) obtained a simplified version of Eq. (1) by setting x ¼ 0, i.e., a point source O2 ¼ 4pf1 cosðy0 Þg.
(2)
Ruby (1994) presented the problem as an integral of Bessel functions of the following form: O¼ Fig. 1. Geometrical arrangement of the coaxial source–detector assembly.
Rd Rs
Z 0
1
k1 ekd J 1 ðkRs ÞJ 1 ðkRd Þ dk
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
116
for which he obtained the following closed-form approximation as a solution
r2 3 x2 r 2 O3 ¼ 4p þ 1 4 d 2d 8d 2 x2 r 2 5 x 4 r 4 þ þ þ3 8 d 2d d 2d x2 r 2 35 x 6 r 6 þ þ6 64 d 2d d 2d 2 2 x r þ . d 2d
ð3Þ
A clinical nuclear camera (Elscint APEX SP-4, Israel) containing a NaI(Tl) detector crystal of approximately 39 cm in diameter and a 36.5 cm diameter Co-57 source (GE Healthcare model CTRF 10051, Mississauga, ON, Canada) at source–detector distances of 50, 100, and 150 cm were used for this investigation. The solid angle subtended by the detector was computed using the three equations above. It has previously been determined that the average value of Eqs. (1)–(3), OAv123, is adequate to describe the solid angle C and thus, these values have been used for calculations (Galiano and Rodrigues, 2006). A parallelepiped support was constructed out of wood in order to suspend the Co-57 source at the various distances ‘d’ above the detector head
as seen in Fig. 2. A simple plumb bob composed of string and a tiny weight was used to ensure that the source was centered directly over the camera’s detector head. The camera was programed to record five million counts of the 122 keV photons emitted from the Co-57 source with a 710% energy window. Collecting more than five million counts did not significantly improve the image quality. A medium and a high-resolution collimator were used separately to image the source at each height d. These parallel-hole collimators contain lead septa that in effect, attempt to resolve the source by attenuating non-perpendicular photons that are incident on the detector head. Although the exact dimensions of individual septa in the collimators are unknown, there is a clear difference seen in the results between the high-resolution and mediumresolution collimators. These differences are analyzed in Section 3. The time and count rate of each individual image acquisition can be found in Table 1. The extrinsic counting efficiency e is defined as the number of counts ‘N’ recorded by the detector in a certain time interval ‘t’, divided by the number of counts ‘NTH’ that theoretically strike the detector surface in that same time interval, with a collimator in place. To determine e, the geometric efficiency G defined as C/4p, had to be computed (Galiano and Rodrigues, 2006). We also require that the activity ‘A’ of the source be known, which for this work was 5.5 mCi70.7%. Finally, the gamma photon emission probability ‘F’ for the decay of Co-57 is 85.6%. Using these parameters, the extrinsic counting efficiency for 122 keV photons for a distributed source is given by ¼
N N4p . ¼ N TH CFAt
(4)
The extrinsic sensitivity ‘s’, is defined as the count rate per unit source activity at a certain distance, also with the
Table 1 The source–detector distance, collimator used, total counts recorded, total acquisition times, and count rates Distance of source from detector (cm)
Collimator used
Total number of counts recorded
Acquisition time (s)
Count rate (counts/s)
50
Medium resolution High resolution
5 106
153
32,680
327
15,291
Medium resolution High resolution
170
29,412
372
13,441
Medium resolution High resolution
178
28,090
397
12,594
100
150 Fig. 2. Experimental setup used where ‘x’ is the source diameter, ‘r’ is the detector diameter, and ‘d’ is the source–detector distance.
ARTICLE IN PRESS M. Rodrigues, E. Galiano / Applied Radiation and Isotopes 65 (2007) 114–119
collimator in place. In mathematical terms N . (5) At The parameters used in Eqs. (4) and (5) are not absolute and therefore have inherent uncertainties. The uncertainty in N, sN, was experimentally determined to be 712000 since this value was the approximate minimum number of counts recorded per second when acquiring data, as seen in Table 1. The uncertainty in time st was 70.5 s. The manufacturer of the Co-57 source has quoted an uncertainty in the source activity of 0.7%. Finally, the uncertainty in the solid angle C was determined to be a ratio of half of the smallest unit of measure divided by the total diameter of the detector head. This gives sC ¼ 7(0.5 cm/39.0 cm) ¼ 70.0128 steradians.
s¼
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source–detector distance. This was in fact observed, as seen in Table 2. For example, as the source-detector distance increases from 50 to 100 cm and then to 150 cm, the sensitivity decreases from 5941 to 5347 counts/s-mCi, and to 5107 counts/s-mCi, respectively, for the medium-resolution collimator. This result is rather simple to predict if one considers that the solid angle decreases with distance. This causes the theoretical number of photons striking the detector surface to decrease, and therefore causes the number of photons actually counted to also decrease. The average uncertainty in the sensitivity of this collimator was determined to be approximately 724 counts/s-mCi, which is less than 1% of the measured sensitivity at any of the three distances. The same general trends are verified for the high-resolution collimator. Fig. 3 shows a graphical
3. Results and discussion Table 1 contains acquired data and Table 2 contains calculated values for the extrinsic counting efficiency and extrinsic sensitivity, as well as their associated uncertainties. Examining Table 1, as the source–detector distance increases from 50 cm, through 100 cm, and then to 150 cm, the acquisition time increased from 153 to 170 s, and then 173 s, respectively, for the medium-resolution collimator. This is not unexpected since the value for the solid angle decreases from 0.6454 to 0.2181 steradians and to 0.1019 steradians, respectively. This decrease in the average solid angle is responsible for the decrease in the counting rate as the source–detector distance is increased. These trends are observed for both the medium and high resolution collimator and a ratio of approximately 2:1 is apparent between the two collimators for the acquisition time as well as the count rate. Since the count rate varies inversely with source–detector distance, one would expect from Eq. (5) that the sensitivity would also decrease with an increase in
Fig. 3. Extrinsic sensitivity versus source–detector distance for both medium and high-resolution collimators. Values for the medium-resolution collimator are approximately twice those of the high-resolution collimator.
Table 2 The source–detector distance, collimator used, average solid angle, extrinsic counting efficiency and extrinsic sensitivity and their corresponding uncertainties Source–detector distance (cm)
Collimator used
Average solid angle (steradians)
Extrinsic counting efficiency (%)
Uncertainty in extrinsic counting efficiency (7%)
Extrinsic sensitivity (counts/s/mCi)
Uncertainty in extrinsic sensitivity (7counts/s-mCi)
50
Medium resolution High resolution
0.6454
0.365
7.394 105
5941.771
25.273
0.17
3.424 105
2780.095
20.855
Medium resolution High resolution
0.2181
0.972
5.723 104
5347.594
24.272
0.445
2.613 104
2443.793
20.541
Medium resolution High resolution
0.1019
1.989
2.500 103
5107.252
23.887
0.891
1.121 103
2289.902
20.409
100
150
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representation of the approximate 2:1 sensitivity ratio between the medium and high-resolution collimators. For the medium-resolution collimator, as the source–detector distance increases from 50 to 100 cm then to 150 cm, the counting efficiency increases from 0.365% to 0.972% then to 1.989%. The average uncertainty was calculated to be 71.049 103%, again within 1% of the measured values. The high-resolution collimator follows the same general trend. In the case of the high-resolution collimator, the average uncertainty was approximately 74.722 104%, also within 1% of the measured values. Fig. 4 shows the efficiency trends for the medium and high-resolution collimators. In principle, the extrinsic counting efficiency should be independent of source-to-detector distance. To further investigate our apparently contradictory results for efficiency, the experimental setup was altered in two ways. First, the Co-57 source was placed directly on top of the collimator, i.e., a d ¼ 0 situation. Second, the collimator was removed from the detector head and the source was placed at d ¼ 50 cm. In both cases, the camera registered approximately five counts in the first few seconds of acquisition. As the acquisition time continued, the number of counts did not increase by any significant amount, and the acquisition was stopped. These results have led us to believe that machine paralysis, specifically a paralyzable model, is occurring in our camera and may partially explain our results (Knoll, 2000). Each time a gamma photon interacts with the detector crystal, a certain amount of time is needed for the camera’s electronics to record that interaction and display it on the image screen. Since the camera’s electronics are insensitive to any photon interaction during this fixed period, this time has been labeled the dead time (t). In paralyzable dead time, any interactions that take place in the fixed period t will extend the dead time by another period t. The actual value of t is not
known for the camera used in this investigation, but modification of the setup has shown that it is clearly long enough to be affected by count rates that are of the order of 104 counts/s. The problem of somehow accounting for dead time losses has received considerable attention in the past. Glass and Vernon (1972) developed a method based on a technique described by Anders (1969) that modifies the electronics of the camera in order to estimate the total counting losses that occur in the system. Madsen and Nickles (1986) were able to correct count-rate losses by comparing the ratio of the count rate from a reference source to data from the reference source fitted to a paralyzable model of dead time. Adams and Mena (1988) used an algorithm and two Fortran programs to accurately determine the dead time of a scintillation camera using a short-lived radionuclide and multiple copper filters. Recently, Mowlavi et al. (2006) developed a Monte Carlo code using Fortran PowerStation 4.0 software to correct pile-up distortion in gamma camera spectroscopy. This Monte Carlo code demonstrated that the Siemens e.Cam gamma camera acts as a paralyzable system in high true count rate, rather than as a non-paralyzable system. This code can also be used with other cameras that have different counting systems in order to correct pile-up. In our work, we have made no systematic effort to compensate for dead time losses. 4. Conclusions The experimental feasibility of measuring the extrinsic counting efficiency and sensitivity of a nuclear medical gamma camera with a large source has been demonstrated. The results show that the sensitivity more or less follows a general inverse square relationship with respect to source–detector distance as expected from simple geometrical considerations. However, the extrinsic counting efficiency increased with an increase in source–detector distance—an unexpected result that we attribute to dead time effects. It is apparent that even at large source–detector distances, the phenomenon of dead time becomes a significant factor at high count rates i.e., in the order of 104 counts/s. Furthermore, the results show an approximate 2:1 ratio in both sensitivity and efficiency between the medium and high-resolution collimators. References
Fig. 4. Extrinsic efficiency versus source–detector distance for both medium and high-resolution collimators. The same approximate 2:1 ratio between collimators seen in the sensitivity (Fig. 3) holds for the efficiency.
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