- Email: [email protected]
Performance of triple coincidence imaging as an addition to dedicated PET
ARTICLE IN PRESS
Radiation Physics and Chemistry 76 (2007) 351–356 www.elsevier.com/locate/radphyschem
Performance of triple coincidence imaging as an addition to dedicated PET Elfatih Abuelhiaa,, K. Kacperskib, S. Kafalaa, N. M Spyroua a Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK Institute of Nuclear Medicine, University College London, Middlesex Hospital, London W1T 3AA, UK
b
Abstract In this work, we investigate the performance of semiconductor detectors imaging capabilities in three-photon annihilation processes in order to combine this novel imaging modality with conventional positron emission tomography. The spatial resolution is studied as a function of detector positions and selected energy window. This was measured from different experimental arrangements and found to be in the range between 3.3–3.9 cm with a mean of 3.570.1 cm. Scatter and random events, coincidence timing resolution and count rate performance are discussed. r 2006 Elsevier Ltd. All rights reserved.
1. Introduction Positron emission tomography (PET) is a functional imaging technique to measure the concentration of radioactivity in body organs to study biological processes. Radioisotopes can label metabolically active compounds and can be used for imaging a number of metabolic processes. The quantification of functional imaging with PET, especially for small structures requires improvements in instrumentations to enhance imaging performance (Zaidi and Sossi, 2004). The challenge for advanced PET instrumentation is the optimization of the performance in terms of spatial resolution, contrast and sensitivity, at minimized fabrication and operation cost of the PET scanner (Phelps and Cherry, 1998). In gamma ray imaging applications, direct detection of g-rays by semiconductor materials offers several advantages over conventional scintillation based detectors. HPGe detectors have good energy resolution. Their use for a dedicated small animal PET system have been investigated (Philips et al., 2002). Corresponding author. Fax: +44 1483686781.
E-mail address: [email protected] (E. Abuelhia).
Semiconductors like CdZTe that can be operated at room temperature could improve PET imaging technology (Moses et al., 1994).
2. Theory and model Recently the usefulness of three-photon annihilation events has been demonstrated (Kacperski et al., 2004). The information gained per event was significantly higher than that in case of the two-photon annihilation. Three-photon annihilation in matter depends on the rates of positronium formation, which in turn depends on the local physical and chemical environment, particularly the existence of oxygen. Three-photons imaging could provide valuable information on the state of oxygenation in tumours (presence of hypoxia). By considering a three-photon decay event that occurs at a point r ¼ ðx; y; zÞ (Fig. 1), the three annihilation photons can have energies between 0 and 511 keV, fulfilling the laws of energy and momentum conservation. If the three photons of energies E1, E2, E3 are detected in coincidence by three detectors, then from
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2006.03.066
ARTICLE IN PRESS 352
E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
Fig. 1. Three-photon annihilations imaging. Each detector generates pulse, which passes to a time pick-off units. Timing signals from the pick-off units are passed to a coincidence unit with timing window of t. If pulses overlap, then logic signal is generated and passed as a trigger to the simultaneous sampling analogue-to-digital- converter (ADC).
he momentum conservation law we get E 1 x x1 E 2 x x2 E 3 x x3 þ þ ¼ 0, c cjr r1 j c cjr r2 j c cjr r3 j E 1 y y1 E 2 y y2 E 3 y y3 py ¼ þ þ ¼ 0, c cjr r1 j c cjr r2 j c cjr r3 j E 1 z z1 E 2 z z2 E 3 z z3 pz ¼ þ þ ¼ 0, c cjr r1 j c cjr r2 j c cjr r3 j
3. Analytical model for triple coincidence technique
px ¼
ð1Þ
and from the law of energy conservation E 1 þ E 2 þ E 3 ¼ 2me c2 1022 keV,
(2)
where me is the electron rest mass. With known detector positions, r1, r2, and r3, the measurement of energies E1, E2, and E3 enables the solution of the non-linear set of Eq. (1) to determine the point r, the position where the annihilation took place. Spatial resolution refers to the blurring of an image of an object due to system limitations. It is characterized by measuring the width of the profile obtained when an object is much smaller than the anticipated resolution of the system. The spatial resolution (FWHM) can be approximated using a Gaussian function ðs ¼ FWHM=2:35Þ where s is the standard deviation of the Gaussian function.
In considering a uniform object containing activity, A (in Becquerel, Bq), we assume the singles rate of the three-photons in a detector (with negligible dead time), can be expressed as Rs ¼ e341 Af bþ Ot expðmLs Þ , where e341 is the window efficiency (the fraction of photons of energy 341 keV when each has equal energy incident on detectors that give rise to a signal that satisfies the energy window constraints), f bþ is the positron decay fraction, m is the linear attenuation coefficient of the object medium and Ls is the path length which leads to the average attenuation in a single event. Os is the average fraction of 4p solid angle subtended by detectors for single photon. The true triple coincidence rate (in case of symmetry), Rt , can be similarly written as Rt ¼ e3341 Af bþ Ot expð3mLt Þ ¼ e3341 K t .
(3)
Ot is different from Os because of an angular restriction on the detection of the three photons, and the path length producing the average attenuation is also different from the singles case. The product of the coincidence resolving time and the singles rates cubed in any three detectors gives the random coincidence
ARTICLE IN PRESS E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
rate, Rr. Rr ¼
4t2r e3341 A3 f 3bþ O3s expð3mLs Þ
353
4. Materials and methods ¼
4t2r e3341 K 3r ,
(4)
where tr is the detector resolving time (coincidence window 2tr ) and K r ¼ Af bþ Os expðmLs Þ. In triple coincidence setting, the system dead time may be related to coincidence rates and adequately characterized by a paralyzable dead time, td, which reduces the count rate that could be measured without dead time, R, by a factor exp (Rt td) (Knoll, 2001), where Rt is the total coincidence count rate, due to true and random counts. Putting this factor into Eq. 3) we obtain the dead timecorrected true coincidence rate Rt ¼ e3341 K t expððK t þ 2tr K 3r Þe3341 td Þ.
4.1. Delayed coincidence channel estimation
(5)
Similarly, Eq. (4) can be modified to obtain the dead time-corrected random coincidence rate Rr ¼ 4t2r e3341 K 3r expððK t þ 2tr K 3r Þe3341 td Þ.
Three HPGe detectors were arranged in a plane forming angles of about 1201 with respect to each other to form a primitive 3g scanner (Fig. 1). In order to have high 3g yields, thin kapton foil encapsulated point-like 22 Na sources have been placed in fine silica powder and sealed in glass containers under nitrogen atmosphere. The triple coincidence events were identified with a lower timing resolution window of 38 ns. The energies in the three channels were registered by a simultaneous sampling ADC.
(6)
The count rate of random events from triple coincidence technique can be estimated by applying to each channel a different time delay so that the time delay differences between detector pairs are larger than the coincidence time window (delay method) (Peter, 2003).
Fig. 2. The circles A, B and C represent the HPGe detector’s positions with respect to a reference point in (x, y) plane. a, b are threephoton images reconstructed as described in image reconstruction section and c, d are their filtered images with FWHM of 3.41 and 3.73 cm respectively. In 2a the timing resolution was 20 ns where as in 2b the timing resolution was 50 ns.
ARTICLE IN PRESS E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
354
given in Eq. (2) is performed. Using Eq. (1) series of rj can be obtained, and the proper image constructed. The image formed as a set of dots (Fig. 2), each one corresponding to single 3g decay. It is clear that the location of the annihilation broadens into a region surrounding the point r; this broadening (point spread) is due to detector energy resolution and size and is a combination of errors in photon energy and position detection. The spatial resolution values were calculated from different experimental arrangements and were found in the range between 3.3 to 3.9 cm with a mean of 3.570.1 cm. The spatial resolution could be improved by narrowing the energy window around the 341 keV peak on the expense of sensitivity. The coincidence timing spectra were measured to determine the coincidence timing resolution of the HPGe detectors when irradiated with 22Na photons, as a function of energy and detector positions. The timing coincidence resolution was 53.170.5 ns when both detectors are 10 cm apart from the source and was 38.670.2 ns when the detectors are 3 cm apart. Table 1 shows the effect of energy window and detector position on 3g events. The optimum position for 3g events to be detected is when the detectors are 13 cm from the source. Putting
This delay removes the correlation between pairs of events arising from single annihilations. Therefore, the detected delayed coincidences are inevitably random. 4.2. Image reconstruction Image reconstruction in three-photon annihilation is very simple compared to 2g PET which is complex. It is required only to solve numerically the non-linear Eq. (1) to retrieve r from a three-photon event. This is done for each event independently, so the reconstruction can be made on-line as new events registered; no need to wait for full image registration. It has been demonstrated that the simple system of three high-energy resolution detectors is able to produce images of 3g annihilations with fairly good accuracy (Abuelhia et al., 2005). 5. Results and discussion The result is a set of triple energies (E1, E2, and E3) obtained in each of the detectors. In order to extract the events corresponding to full-peak detected 3g annihilations, filtering in which only events with all E i o511 keV and fulfilling the condition of energy conservation
Table 1 The effect of windows set-up and distances on total registered events Distances (source to detector) 71 cm
9.0 13.0 17.0
Total events registered
Energy window 5 keV
775 303 214 615 130 005
10 keV
15 keV
20 keV
25 keV
3g
%
3g
%
3g
%
3g
%
3g
%
2573 1649 1037
0.3 0.8 0.8
5152 3280 1820
0.7 1.5 1.4
7262 4189 2246
0.9 2.0 1.7
8877 4894 2603
1.1 2.3 2.0
10299 5467 2872
1.3 2.5 2.2
Column one shows detectors positioned at different distances from the source (22Na: 0.361 MBq, 72 h acquisition time), to see the effect of scanner size on detection of three-photon annihilation. Total events are the events registered and include true events (3g) and scattered events (accidental events; from 511 keV and prompt 1274 keV which are partially detected).
Table 2 Delay coincidence technique (estimation of random events count rate) Triple coincidence exp.
Total count rate (c/s)
3g Events (%)
SEo1022 (%)
SE41022 (%)
(1 511) (%)
(2 511) (%)
1 1a 1b 2 2a
0.147 0.129 0.122 8.47 2.686
2.3 0.5 0.5 1.2 .4
89.75 98.1 97.8 93.1 98.3
8 1.5 1.8 5.6 1.3
15.9 15.5 15.2 15.4 14.5
1 0.3 0.2 0.9 0.3
Percentages of events are given for which respectively: sum of the energies is smaller than 1022–10 keV (SEo1022), sum of the energies is greater than 1022+10 keV, one of the energies equals 51175 keV and two of the energies are equal to 51175 keV. a Only one channel was delayed. b Tow channels were delayed (with time greater than (2t)).
ARTICLE IN PRESS E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
the detector closer will only increase the accidental events with no improvement in the true 3g events. The count rate of random events from triple coincidence technique was estimated by applying delay technique (Table 2). Fig. 3a shows that the energy resolution is worsen with energy window increase i.e., FWHM deteriorates at higher count rate. Fig. 3b shows the corrected true and random events versus the activity. At higher activity the true three-photon decay rate reduced while the amount of the accidental events
355
increased. The main source of accidental events is due to the double 2g random coincidences, where two 511 keV photons pass through two of the detectors while the third detector is hit by prompt 1274 keV photons of 22Na. 6. Conclusion To introduce the three-photon technique to dedicated PET, high-energy resolution detectors are needed which will improve the quality of the image and reduce the noise
Fig. 3. (A) FWHM and the percentage of 3g versus energy window, and (B) Corrected true and random events versus activity.
ARTICLE IN PRESS 356
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due to scattered events. The accidental coincidences can be easily suppressed by narrowing the energy window around (341 keV) on the expense of the sensitivity. To get a reasonable three-photon image the detectors should not be close or far from the object. The contribution of threephoton attenuation is not discussed here because it is difficult to correct for experimentally. However, it can be assessed by constructing a map of attenuation coefficient.
Acknowledgments Two of the authors would like to thank the International Atomic Energy Agency (IAEA) and Daphne Jackson Trust University of Surrey.
References Abuelhia, E., Kacperski, K., Kafala, S., Spyrou, N.M., 2005. Three-photon annihilation in PET: 2D imaging
experiments. J. Radiat. Nucl. Chem., accepted for publication. Kacperski, K., Spyrou, N.M., Smith, F.A., 2004. Three-gamma annihilation imaging in positron tomography. IEEE Trans. Med. Im. 23, 525–529. Knoll, G.F., 2001. Radiation Detection and Measurement. Wiley, New York. Moses, W.W., Derenzo, S.E., Budinger, T.F., 1994. PET detector modules based on novel detector technologies. Nucl. Instrum. Meth. A 353, 189–194. Phelps, M.E., Cherry, S.R., 1998. The changing design of positron imaging systems. Clin. Pos. Imag. 1, 31–45. Philips, B.F., Kroeger, J.D., Kurfess, J.D., Johnson, W.N., Wulf, E.A., Novikova, E.I., 2002. Small animal PET imaging with germanium strip detectors. IEEE. Nucl. Sci. Symp. Conf. Rec. 3, 1438–1442. Peter, E., 2003. In: Bailey, D., Townsend, D., Maisey, M. (Eds.), Positron Emission Tomography Basic Science and Clinical Practice. Springer, New York, NY, p. 884. Zaidi, H., Sossi., V., 2004. Correction for image degrading factors is essential for accurate quantification of brain function using PET. Med. Phys. 31, 423–426.
Radiation Physics and Chemistry 76 (2007) 351–356 www.elsevier.com/locate/radphyschem
Performance of triple coincidence imaging as an addition to dedicated PET Elfatih Abuelhiaa,, K. Kacperskib, S. Kafalaa, N. M Spyroua a Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK Institute of Nuclear Medicine, University College London, Middlesex Hospital, London W1T 3AA, UK
b
Abstract In this work, we investigate the performance of semiconductor detectors imaging capabilities in three-photon annihilation processes in order to combine this novel imaging modality with conventional positron emission tomography. The spatial resolution is studied as a function of detector positions and selected energy window. This was measured from different experimental arrangements and found to be in the range between 3.3–3.9 cm with a mean of 3.570.1 cm. Scatter and random events, coincidence timing resolution and count rate performance are discussed. r 2006 Elsevier Ltd. All rights reserved.
1. Introduction Positron emission tomography (PET) is a functional imaging technique to measure the concentration of radioactivity in body organs to study biological processes. Radioisotopes can label metabolically active compounds and can be used for imaging a number of metabolic processes. The quantification of functional imaging with PET, especially for small structures requires improvements in instrumentations to enhance imaging performance (Zaidi and Sossi, 2004). The challenge for advanced PET instrumentation is the optimization of the performance in terms of spatial resolution, contrast and sensitivity, at minimized fabrication and operation cost of the PET scanner (Phelps and Cherry, 1998). In gamma ray imaging applications, direct detection of g-rays by semiconductor materials offers several advantages over conventional scintillation based detectors. HPGe detectors have good energy resolution. Their use for a dedicated small animal PET system have been investigated (Philips et al., 2002). Corresponding author. Fax: +44 1483686781.
E-mail address: [email protected] (E. Abuelhia).
Semiconductors like CdZTe that can be operated at room temperature could improve PET imaging technology (Moses et al., 1994).
2. Theory and model Recently the usefulness of three-photon annihilation events has been demonstrated (Kacperski et al., 2004). The information gained per event was significantly higher than that in case of the two-photon annihilation. Three-photon annihilation in matter depends on the rates of positronium formation, which in turn depends on the local physical and chemical environment, particularly the existence of oxygen. Three-photons imaging could provide valuable information on the state of oxygenation in tumours (presence of hypoxia). By considering a three-photon decay event that occurs at a point r ¼ ðx; y; zÞ (Fig. 1), the three annihilation photons can have energies between 0 and 511 keV, fulfilling the laws of energy and momentum conservation. If the three photons of energies E1, E2, E3 are detected in coincidence by three detectors, then from
0969-806X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.radphyschem.2006.03.066
ARTICLE IN PRESS 352
E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
Fig. 1. Three-photon annihilations imaging. Each detector generates pulse, which passes to a time pick-off units. Timing signals from the pick-off units are passed to a coincidence unit with timing window of t. If pulses overlap, then logic signal is generated and passed as a trigger to the simultaneous sampling analogue-to-digital- converter (ADC).
he momentum conservation law we get E 1 x x1 E 2 x x2 E 3 x x3 þ þ ¼ 0, c cjr r1 j c cjr r2 j c cjr r3 j E 1 y y1 E 2 y y2 E 3 y y3 py ¼ þ þ ¼ 0, c cjr r1 j c cjr r2 j c cjr r3 j E 1 z z1 E 2 z z2 E 3 z z3 pz ¼ þ þ ¼ 0, c cjr r1 j c cjr r2 j c cjr r3 j
3. Analytical model for triple coincidence technique
px ¼
ð1Þ
and from the law of energy conservation E 1 þ E 2 þ E 3 ¼ 2me c2 1022 keV,
(2)
where me is the electron rest mass. With known detector positions, r1, r2, and r3, the measurement of energies E1, E2, and E3 enables the solution of the non-linear set of Eq. (1) to determine the point r, the position where the annihilation took place. Spatial resolution refers to the blurring of an image of an object due to system limitations. It is characterized by measuring the width of the profile obtained when an object is much smaller than the anticipated resolution of the system. The spatial resolution (FWHM) can be approximated using a Gaussian function ðs ¼ FWHM=2:35Þ where s is the standard deviation of the Gaussian function.
In considering a uniform object containing activity, A (in Becquerel, Bq), we assume the singles rate of the three-photons in a detector (with negligible dead time), can be expressed as Rs ¼ e341 Af bþ Ot expðmLs Þ , where e341 is the window efficiency (the fraction of photons of energy 341 keV when each has equal energy incident on detectors that give rise to a signal that satisfies the energy window constraints), f bþ is the positron decay fraction, m is the linear attenuation coefficient of the object medium and Ls is the path length which leads to the average attenuation in a single event. Os is the average fraction of 4p solid angle subtended by detectors for single photon. The true triple coincidence rate (in case of symmetry), Rt , can be similarly written as Rt ¼ e3341 Af bþ Ot expð3mLt Þ ¼ e3341 K t .
(3)
Ot is different from Os because of an angular restriction on the detection of the three photons, and the path length producing the average attenuation is also different from the singles case. The product of the coincidence resolving time and the singles rates cubed in any three detectors gives the random coincidence
ARTICLE IN PRESS E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
rate, Rr. Rr ¼
4t2r e3341 A3 f 3bþ O3s expð3mLs Þ
353
4. Materials and methods ¼
4t2r e3341 K 3r ,
(4)
where tr is the detector resolving time (coincidence window 2tr ) and K r ¼ Af bþ Os expðmLs Þ. In triple coincidence setting, the system dead time may be related to coincidence rates and adequately characterized by a paralyzable dead time, td, which reduces the count rate that could be measured without dead time, R, by a factor exp (Rt td) (Knoll, 2001), where Rt is the total coincidence count rate, due to true and random counts. Putting this factor into Eq. 3) we obtain the dead timecorrected true coincidence rate Rt ¼ e3341 K t expððK t þ 2tr K 3r Þe3341 td Þ.
4.1. Delayed coincidence channel estimation
(5)
Similarly, Eq. (4) can be modified to obtain the dead time-corrected random coincidence rate Rr ¼ 4t2r e3341 K 3r expððK t þ 2tr K 3r Þe3341 td Þ.
Three HPGe detectors were arranged in a plane forming angles of about 1201 with respect to each other to form a primitive 3g scanner (Fig. 1). In order to have high 3g yields, thin kapton foil encapsulated point-like 22 Na sources have been placed in fine silica powder and sealed in glass containers under nitrogen atmosphere. The triple coincidence events were identified with a lower timing resolution window of 38 ns. The energies in the three channels were registered by a simultaneous sampling ADC.
(6)
The count rate of random events from triple coincidence technique can be estimated by applying to each channel a different time delay so that the time delay differences between detector pairs are larger than the coincidence time window (delay method) (Peter, 2003).
Fig. 2. The circles A, B and C represent the HPGe detector’s positions with respect to a reference point in (x, y) plane. a, b are threephoton images reconstructed as described in image reconstruction section and c, d are their filtered images with FWHM of 3.41 and 3.73 cm respectively. In 2a the timing resolution was 20 ns where as in 2b the timing resolution was 50 ns.
ARTICLE IN PRESS E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
354
given in Eq. (2) is performed. Using Eq. (1) series of rj can be obtained, and the proper image constructed. The image formed as a set of dots (Fig. 2), each one corresponding to single 3g decay. It is clear that the location of the annihilation broadens into a region surrounding the point r; this broadening (point spread) is due to detector energy resolution and size and is a combination of errors in photon energy and position detection. The spatial resolution values were calculated from different experimental arrangements and were found in the range between 3.3 to 3.9 cm with a mean of 3.570.1 cm. The spatial resolution could be improved by narrowing the energy window around the 341 keV peak on the expense of sensitivity. The coincidence timing spectra were measured to determine the coincidence timing resolution of the HPGe detectors when irradiated with 22Na photons, as a function of energy and detector positions. The timing coincidence resolution was 53.170.5 ns when both detectors are 10 cm apart from the source and was 38.670.2 ns when the detectors are 3 cm apart. Table 1 shows the effect of energy window and detector position on 3g events. The optimum position for 3g events to be detected is when the detectors are 13 cm from the source. Putting
This delay removes the correlation between pairs of events arising from single annihilations. Therefore, the detected delayed coincidences are inevitably random. 4.2. Image reconstruction Image reconstruction in three-photon annihilation is very simple compared to 2g PET which is complex. It is required only to solve numerically the non-linear Eq. (1) to retrieve r from a three-photon event. This is done for each event independently, so the reconstruction can be made on-line as new events registered; no need to wait for full image registration. It has been demonstrated that the simple system of three high-energy resolution detectors is able to produce images of 3g annihilations with fairly good accuracy (Abuelhia et al., 2005). 5. Results and discussion The result is a set of triple energies (E1, E2, and E3) obtained in each of the detectors. In order to extract the events corresponding to full-peak detected 3g annihilations, filtering in which only events with all E i o511 keV and fulfilling the condition of energy conservation
Table 1 The effect of windows set-up and distances on total registered events Distances (source to detector) 71 cm
9.0 13.0 17.0
Total events registered
Energy window 5 keV
775 303 214 615 130 005
10 keV
15 keV
20 keV
25 keV
3g
%
3g
%
3g
%
3g
%
3g
%
2573 1649 1037
0.3 0.8 0.8
5152 3280 1820
0.7 1.5 1.4
7262 4189 2246
0.9 2.0 1.7
8877 4894 2603
1.1 2.3 2.0
10299 5467 2872
1.3 2.5 2.2
Column one shows detectors positioned at different distances from the source (22Na: 0.361 MBq, 72 h acquisition time), to see the effect of scanner size on detection of three-photon annihilation. Total events are the events registered and include true events (3g) and scattered events (accidental events; from 511 keV and prompt 1274 keV which are partially detected).
Table 2 Delay coincidence technique (estimation of random events count rate) Triple coincidence exp.
Total count rate (c/s)
3g Events (%)
SEo1022 (%)
SE41022 (%)
(1 511) (%)
(2 511) (%)
1 1a 1b 2 2a
0.147 0.129 0.122 8.47 2.686
2.3 0.5 0.5 1.2 .4
89.75 98.1 97.8 93.1 98.3
8 1.5 1.8 5.6 1.3
15.9 15.5 15.2 15.4 14.5
1 0.3 0.2 0.9 0.3
Percentages of events are given for which respectively: sum of the energies is smaller than 1022–10 keV (SEo1022), sum of the energies is greater than 1022+10 keV, one of the energies equals 51175 keV and two of the energies are equal to 51175 keV. a Only one channel was delayed. b Tow channels were delayed (with time greater than (2t)).
ARTICLE IN PRESS E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
the detector closer will only increase the accidental events with no improvement in the true 3g events. The count rate of random events from triple coincidence technique was estimated by applying delay technique (Table 2). Fig. 3a shows that the energy resolution is worsen with energy window increase i.e., FWHM deteriorates at higher count rate. Fig. 3b shows the corrected true and random events versus the activity. At higher activity the true three-photon decay rate reduced while the amount of the accidental events
355
increased. The main source of accidental events is due to the double 2g random coincidences, where two 511 keV photons pass through two of the detectors while the third detector is hit by prompt 1274 keV photons of 22Na. 6. Conclusion To introduce the three-photon technique to dedicated PET, high-energy resolution detectors are needed which will improve the quality of the image and reduce the noise
Fig. 3. (A) FWHM and the percentage of 3g versus energy window, and (B) Corrected true and random events versus activity.
ARTICLE IN PRESS 356
E. Abuelhia et al. / Radiation Physics and Chemistry 76 (2007) 351–356
due to scattered events. The accidental coincidences can be easily suppressed by narrowing the energy window around (341 keV) on the expense of the sensitivity. To get a reasonable three-photon image the detectors should not be close or far from the object. The contribution of threephoton attenuation is not discussed here because it is difficult to correct for experimentally. However, it can be assessed by constructing a map of attenuation coefficient.
Acknowledgments Two of the authors would like to thank the International Atomic Energy Agency (IAEA) and Daphne Jackson Trust University of Surrey.
References Abuelhia, E., Kacperski, K., Kafala, S., Spyrou, N.M., 2005. Three-photon annihilation in PET: 2D imaging
experiments. J. Radiat. Nucl. Chem., accepted for publication. Kacperski, K., Spyrou, N.M., Smith, F.A., 2004. Three-gamma annihilation imaging in positron tomography. IEEE Trans. Med. Im. 23, 525–529. Knoll, G.F., 2001. Radiation Detection and Measurement. Wiley, New York. Moses, W.W., Derenzo, S.E., Budinger, T.F., 1994. PET detector modules based on novel detector technologies. Nucl. Instrum. Meth. A 353, 189–194. Phelps, M.E., Cherry, S.R., 1998. The changing design of positron imaging systems. Clin. Pos. Imag. 1, 31–45. Philips, B.F., Kroeger, J.D., Kurfess, J.D., Johnson, W.N., Wulf, E.A., Novikova, E.I., 2002. Small animal PET imaging with germanium strip detectors. IEEE. Nucl. Sci. Symp. Conf. Rec. 3, 1438–1442. Peter, E., 2003. In: Bailey, D., Townsend, D., Maisey, M. (Eds.), Positron Emission Tomography Basic Science and Clinical Practice. Springer, New York, NY, p. 884. Zaidi, H., Sossi., V., 2004. Correction for image degrading factors is essential for accurate quantification of brain function using PET. Med. Phys. 31, 423–426.