REVIEW OF SCIENTIFIC INSTRUMENTS 86, 054301 (2015)
Enhancement of molecular sensitivity in positron emission tomography with quantum correlation of γ-ray photons K. Sato1 and Y. Kobayashi2 1 2
Department of Environmental Sciences, Tokyo Gakugei University, 4-1-1 Koganei, Tokyo 184-8501, Japan National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan
(Received 26 March 2015; accepted 13 May 2015; published online 27 May 2015) Enhancement of molecular sensitivity in positron emission tomography (PET) has long been discussed with respect to imaging instrumentation and algorithms for data treatment. Here, the molecular sensitivity in PET is discussed on the basis of 2-dimensional coincident measurements of 511 keV γ ray photons resultant from two-photon annihilation. Introduction of an additional selection window based on the energy sum and difference of the coincidently measured γ ray photons, without any significant instrumental and algorithmic changes, showed an improvement in the signal-to-noise ratio (SNR) by an order of magnitude. Improvement of performance characteristics in the PET imaging system was demonstrated by an increase in the noise equivalent count rate (NECR) which takes both the SNR and the detection efficiency into consideration. A further improvement of both the SNR and the NECR is expected for the present system in real clinical and in-vivo environments, where much stronger positron sources are employed. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4921714]
I. INTRODUCTION
Positron emission tomography (PET) is a highly sensitive technique for visualizing the distribution of specific molecular targets that are sensitive to diseases such as cancer, heart disease, and neurological disorders.1 In clinical and in-vivo small animal research, positrons from β+ decay radionuclides with short lifetimes, such as 11C, 15O, 18F, and 94mTc, are employed.2 High energy positrons emitted from such radionuclides undergo inelastic and elastic scattering with electrons and nuclei inside the body. Positrons mostly lose their kinetic energy down to the thermal energy of surrounding material ∼kT and eventually annihilate with electrons. The most probable decay channel is two-photon annihilation and less than 1% of positrons annihilate with the emission of three or more photons.3 Molecular imaging with PET is based on two-photon annihilation, where two γ ray photons each with an energy of around 511 keV are emitted in opposite directions to conserve momentum. In PET imaging, two γ ray photons with energies in the vicinity of 511 keV are measured in coincidence by two collinearly aligned γ-ray detectors. Detection of two γ-ray photons by a detector pair within a certain coincidence-time window is regarded as a valid event for PET imaging, defining a line of response (LOR) that is the straight line connecting the two detectors.4 The position of the molecular target of interest is determined accurately by accumulation of LOR data, since the positron annihilation site is located on the intersection point of a number of LORs. Next-generation PET imaging requires an increase by an order of magnitude in the detection and visualization performance for small targets at low concentrations, hereafter referred to as the molecular sensitivity.5 The molecular sensitivity is determined by a combination of the biophysical properties of the target and the performance characteristics of 0034-6748/2015/86(5)/054301/4/$30.00
the imaging system. Coincident events between detector pairs generally contain unwanted events irrelevant to two-photon annihilation γ-ray quanta, which deteriorates the SNR and consequently reduces the sensitivity of PET.6 One source of such unwanted events is caused by annihilation γ-rays which are Compton scattered away from the traveling direction resulting in a false LOR. Another is accidental (random) coincidence events, where two γ ray photons from different annihilations are detected at approximately the same time. Similarly to accidental coincidence events, three events from two annihilations by chance counted within the coincidencetime window, known as multiple coincidence events, also yield a false signal. Enhancement of the molecular sensitivity in PET imaging has long been discussed with respect to imaging instrumentation and algorithms for data treatment.7 Geometrical collimation of γ-rays8 or replacement of γ-ray detectors with high purity Ge detectors9 improves the spatial resolution. Both of these techniques, however, reduce the detection efficiency of γ-ray photons and enhance statistical fluctuations, reducing the molecular sensitivity in PET imaging. Use of smoothing treatments for improving statistical fluctuations, on the contrary, deteriorates the spatial resolution.10 In this study, the molecular sensitivity in PET imaging is explored by means of 2-dimensional (2D) coincident measurements of γ ray photons from two-photon annihilation. A method for enhancing molecular sensitivity in PET imaging based on the quantum correlation of γ ray photons is proposed. II. PRINCIPLE OF PET IMAGING WITH QUANTUM CORRELATION OF γ RAY PHOTONS
In PET imaging, the energies of the two annihilation γray photons emitted at 180◦ are measured in coincidence by two intrinsic γ-ray detectors.4 The energies of the two γ-ray
86, 054301-1
© 2015 AIP Publishing LLC
054301-2
K. Sato and Y. Kobayashi
Rev. Sci. Instrum. 86, 054301 (2015)
FIG. 1. X-Y 2D presentation of energy resolution with a diameter of δ E (green circle), a box-shaped energy window with a side of δ E (blue square), and an additional box-shaped energy window with a side of δ E (red square) introduced by the quantum correlation of the coincidently measured γ-ray photons following Eqs. (5) and (6). The center corresponds to (511, 511) in the X-Y coordinate. The black solid and dotted lines correspond to E 1 + E 2 = 2m 0c 2 and E 1 − E 2 = 0, respectively. FIG. 2. Schematic diagram of the present experimental setup.
photons E1 and E2 are described as E1 = m0c2 + δE,
(1)
E2 = m0c2 − δE,
(2)
where m0, c, and δE are rest mass of the electron, the velocity of light, and the energy resolution, respectively. Fig. 1 shows a 2D schematic representation of the energies of the two γray photons coincidently measured. In this representation, the energy resolution of the 2D system is described as a green circle with a diameter of δE centered at X = 511, Y = 511. This circle is referred to as the resolution circle hereafter. In conventional PET imaging, each of the two coincident γrays is independently energy selected, which corresponds to the selection of the events that fall in a box-shaped energy window with a side of δE (see the blue square). In this case, the events in the regions outside the resolution circle, indicated by gray triangles denoted as A in Fig. 1, are included in the valid events but they are likely false signals causing noise in PET images. To reduce the coincident events in the regions A, the following quantum correlation of two γ-ray photons is introduced in addition to the conventional coincidence method. Equations (1) and (2) yield the sum energy ΣE and difference energy ∆E as E = E1 + E2 = 2m0c2, (3) ∆E = E1 − E2 = 2δE.
(4)
Equation (3) indicates the straight line passing through the center of resolution circle (511, 511) with a gradient of −1 (see the black solid line in Fig. 1), whereas E1 − E2 = 0 available from Eq. (4) passes through (511, 511) with a gradient of 1 (see the black dotted line in Fig. 1). Here, a box-shaped energy window with a side of δE indicated by the red square is additionally set by introducing the quantum correlation of the coincidently measured γ-ray photons following Eqs. (5) and (6) below, √ √ 2 2 δE < E1 − E2 < δE, (5) − 2 2
√
√ 2 2 1022 − δE < E1 + E2 < 1022 + δE. (6) 2 2 The coincident events within an octagon-shape energy window are now energy-selected, instead of those in the blue square, which results in the elimination of the false coincident events in the regions A.
III. EXPERIMENTAL SETUP
Fig. 2 shows a schematic diagram of the present experimental setup. 511 keV γ rays emitted as a result of positron annihilation in the samples are detected by scintillators coupled with photomultiplier tubes (PMT1 and PMT2). Two scintillators of Bi4Ge3O12 (BGO) each with a diameter of 1 in. and a thickness of 1 in. were used. PMT1 and PMT2 were collinearly aligned to each other mimicking a real pair of γ ray detectors in a PET system. A 22Na positron emitter with a source strength of ∼10−1 MBq sealed in a thin foil of kapton was mounted in a sample-source-sample sandwich. Two identical discs of single-crystalline Al were employed as samples. Analog pulses from PMT1 and PMT2 were transferred to a 2D-multichannel analyzer (2D-MCA) with a built-in ADC through an amplifier (AMP). Pairs of correlated digital outputs within a coincident time of 300 ns were stored in random-access-memory and displayed as a 2D image, controlled by a personal computer (PC).
IV. RESULTS AND DISCUSSION
Fig. 3 shows a 2D X-Y presentation of the coincidently measured γ ray photons, in which the center of the circle is the peak arising from two-photon annihilation, thus corresponding to the X-Y coordinate (511, 511). The fingerprint-like images at lower energy regions perpendicular to the X (E1) and Y (E2) axes are caused by incomplete charge collection and Compton scattering. A box-shaped energy window with a
054301-3
K. Sato and Y. Kobayashi
FIG. 3. X-Y 2D presentation of two γ ray photons. The blue square-shaped energy window corresponds to the energy window of a conventional PET system and an additional energy window, introduced based on the quantum correlation between the two γ ray photons is shown with the red square. The center of these squares is the peak arising from two-photon annihilation, thus corresponding to an X-Y coordinate of (511, 511). The coincident counts are highest here at this center point.
Rev. Sci. Instrum. 86, 054301 (2015)
spectrum obtained by introducing the quantum correlation of coincidently measured γ ray photons is an order of magnitude higher than that in conventional PET, demonstrating that the present method is able to improve the molecular sensitivity of PET imaging. The background due to accidental and scattered coincident events in the 1D γ ray energy spectrum is efficiently reduced in the vicinity of the energy-box windows in comparison with that by collimation of γ-ray photons of ∼0.01%.8 It is furthermore noted that the sensitivity of positron images can be improved by simply introducing the energy correlation between the two γ-ray photons without any significant instrumental changes. In principle, the SNR and the detection efficiency in PET imaging have a trade-off relationship, i.e., an increase in one leads to a reduction in the other and vice versa. The performance characteristics of PET imaging are thus often examined by the noise equivalent count rate (NECR)11 given by N EC R =
T2 , T2 + R + S
(7)
side of 200 ch (0.6 keV/ch) drawn as a blue square corresponds to the energy window of a conventional PET system, and thus contains false coincident events in the regions outside the resolution circles. Following Eqs. (5) and (6), a box-shaped energy window with a side of 200 ch was additionally set at the center of the resolution circle (511, 511), as drawn as a red square. This box-shaped energy window (rotated by π/4 compared to the conventional energy window) corresponds to an additional energy window based on the quantum correlation of the coincidently measured γ ray photons, i.e., the sum and difference of energies of the two photons. Fig. 4 shows (a) the projected 1D γ ray energy spectrum onto x-axis in the conventional (blue) box-shaped energy window and (b) that onto the diagonal-axis in the octagon-shaped energy window formed by the combination of both (blue and red) box-shaped windows. The projected energy spectrum onto the x-axis in the box-shaped energy window and that onto diagonal-axis in the octagon-shaped energy window correspond to conventional and present PET, respectively. Obviously, the SNR in the 1D γ ray energy
where T, R, and S are the true, random (accidental), and scattered coincidence count rates, respectively. As mentioned above, the present method based on the quantum correlation of γ ray photons sufficiently reduces the background due to random (R) and scattered (S) coincident events (see Fig. 4). From Eq. (7), it is seen that the value of NECR thus increases, demonstrating an improvement of the present system with respect both to the SNR and the detection efficiency. Generally, PET imaging in clinical and in-vivo small animal research is performed by employing a strong positron source more than ∼103 MBq with a short half-life in order to avoid excessive radiation exposure to the subject.12 The background level arising from random (R) and scattered (S) coincident events could be higher than that with the positron source of ∼10−1 MBq demonstrated here. A further improvement of both the SNR and the NECR is thus expected for the present system in real clinical and in-vivo environments. It is noted that enhancing the molecular sensitivity is a subject of interest in any PET imaging system, including time-of-flight (TOF)-PET13 and depth-of-interaction (DOI)PET.14 The TOF-PET technique requires fast scintillators such as, e.g., Lu2SiO5:Ce (LSO) and BaF2 with a fast decay time for achieving excellent time resolution. We have already succeeded in applying the proposed method for the PET imaging system with BaF2 scintillators.15 In addition, the present method can be utilized for PET imaging systems with different detectors such as high purity Ge detectors, which have been used to improve the spatial resolution down to 1 mm.9 We propose that the present method based on the quantum correlation of γ ray photons is not only simple but also universally applicable for any PET imaging system with different scintillators, detectors, application specific integrated circuits (ASICs), and so on.
FIG. 4. (a) Projected energy spectra into the x-axis (black solid line) and (b) the diagonal-axis (red solid line) in the box energy windows. The projected energy spectra into x-axis and diagonal-axis in the box energy windows correspond to conventional and present PET, respectively.
V. CONCLUSIONS
Molecular sensitivity in PET imaging was studied by 2D coincident measurements of positron annihilation 511 keV
054301-4
K. Sato and Y. Kobayashi
γ ray photons resultant from two photon annihilation. By introducing constraints based on the quantum correlation of the coincidently measured γ ray photons, i.e., the sum and difference energies of the photons, a box-shaped energy window, which is rotated by π/4 from conventional window, was additionally set around the peak center (511, 511) in addition to the conventional window. This reduces the noise originating from the false coincident events in the regions outside the resolution circle, by leading to an increase in the SNR by an order of magnitude compared to a conventional system. The improvement of performance characteristic in the PET imaging system was further demonstrated by an increase in the NECR, a metric which takes account of both the SNR and the detection efficiency. ACKNOWLEDGMENTS
We are grateful to Dr. Brian E. O’Rourke of the National Institute of Advanced Industrial Science and Technology for proof-reading the manuscript. This work was partially supported by a Grant-in-Aid of the Japanese Ministry of
Rev. Sci. Instrum. 86, 054301 (2015)
Education, Science, Sports and Culture (Grant Nos. 21540317 and 23740234). 1S.
S. Gambhir, Nat. Rev. Cancer 2, 683 (2002). W. Miller, N. J. Long, R. Vilar, and A. D. Gee, Angew. Chem., Int. Ed. 47, 8998 (2008). 3M. D. Harpen, Med. Phys. 31, 57 (2004). 4Positron Emission Tomography: Basic Sciences, edited by D. L. Bailey, D. W. Townsend, P. E. Valk, and M. N. Maisey (Springer-Verlag, London, Limited, 2005). 5C. S. Levin, Proc. IEEE 96, 439 (2008). 6A. K. Shukla and J. Utham kumar, Med. Phys. 31, 13 (2006). 7H. Peng and C. S. Levin, Curr. Pharm. Biotechnol. 11, 555 (2010). 8A. Rahmim and H. Zaidi, Nucl. Med. Commun. 29, 193 (2008). 9K. Ishii, Y. Kikuchi, S. Matsuyama, Y. Kanai, K. Kotani, T. Ito, H. Yamazaki, Y. Funaki, R. Iwata, M. Itoh, K. Yanai, J. Hatazawa, N. Itoh, N. Tanizaki, D. Amano, M. Yamada, and T. Yamaguchi, Nucl. Instrum. Methods Phys. Res., Sect. A 576, 435 (2007). 10A. M. Alessioa and P. E. Kinahan, Med. Phys. 33, 4095 (2006). 11S. C. Strother, M. E. Casey, and E. J. Hoffman, IEEE Trans. Nucl. Sci. 37, 783 (1990). 12C. G. Rhodes and J. M. B. Hughes, Eur. Respir. J. 8, 1001 (1995). 13K. Ishii, H. Orihara, T. Matsuzawa, D. M. Binkley, and R. Nutt, Rev. Sci. Instrum. 61, 3755 (1990). 14M. Soret, S. L. Bacharach, and I. Buvat, J. Nucl. Med. 48, 932 (2007). 15K. Sato and Y. Kobayashi, Japanese patent 4997603 (2012). 2P.
Review of Scientific Instruments is copyrighted by AIP Publishing LLC (AIP). Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. For more information, see http://publishing.aip.org/authors/rights-and-permissions.
Enhancement of molecular sensitivity in positron emission tomography with quantum correlation of γ-ray photons K. Sato1 and Y. Kobayashi2 1 2
Department of Environmental Sciences, Tokyo Gakugei University, 4-1-1 Koganei, Tokyo 184-8501, Japan National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8568, Japan
(Received 26 March 2015; accepted 13 May 2015; published online 27 May 2015) Enhancement of molecular sensitivity in positron emission tomography (PET) has long been discussed with respect to imaging instrumentation and algorithms for data treatment. Here, the molecular sensitivity in PET is discussed on the basis of 2-dimensional coincident measurements of 511 keV γ ray photons resultant from two-photon annihilation. Introduction of an additional selection window based on the energy sum and difference of the coincidently measured γ ray photons, without any significant instrumental and algorithmic changes, showed an improvement in the signal-to-noise ratio (SNR) by an order of magnitude. Improvement of performance characteristics in the PET imaging system was demonstrated by an increase in the noise equivalent count rate (NECR) which takes both the SNR and the detection efficiency into consideration. A further improvement of both the SNR and the NECR is expected for the present system in real clinical and in-vivo environments, where much stronger positron sources are employed. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4921714]
I. INTRODUCTION
Positron emission tomography (PET) is a highly sensitive technique for visualizing the distribution of specific molecular targets that are sensitive to diseases such as cancer, heart disease, and neurological disorders.1 In clinical and in-vivo small animal research, positrons from β+ decay radionuclides with short lifetimes, such as 11C, 15O, 18F, and 94mTc, are employed.2 High energy positrons emitted from such radionuclides undergo inelastic and elastic scattering with electrons and nuclei inside the body. Positrons mostly lose their kinetic energy down to the thermal energy of surrounding material ∼kT and eventually annihilate with electrons. The most probable decay channel is two-photon annihilation and less than 1% of positrons annihilate with the emission of three or more photons.3 Molecular imaging with PET is based on two-photon annihilation, where two γ ray photons each with an energy of around 511 keV are emitted in opposite directions to conserve momentum. In PET imaging, two γ ray photons with energies in the vicinity of 511 keV are measured in coincidence by two collinearly aligned γ-ray detectors. Detection of two γ-ray photons by a detector pair within a certain coincidence-time window is regarded as a valid event for PET imaging, defining a line of response (LOR) that is the straight line connecting the two detectors.4 The position of the molecular target of interest is determined accurately by accumulation of LOR data, since the positron annihilation site is located on the intersection point of a number of LORs. Next-generation PET imaging requires an increase by an order of magnitude in the detection and visualization performance for small targets at low concentrations, hereafter referred to as the molecular sensitivity.5 The molecular sensitivity is determined by a combination of the biophysical properties of the target and the performance characteristics of 0034-6748/2015/86(5)/054301/4/$30.00
the imaging system. Coincident events between detector pairs generally contain unwanted events irrelevant to two-photon annihilation γ-ray quanta, which deteriorates the SNR and consequently reduces the sensitivity of PET.6 One source of such unwanted events is caused by annihilation γ-rays which are Compton scattered away from the traveling direction resulting in a false LOR. Another is accidental (random) coincidence events, where two γ ray photons from different annihilations are detected at approximately the same time. Similarly to accidental coincidence events, three events from two annihilations by chance counted within the coincidencetime window, known as multiple coincidence events, also yield a false signal. Enhancement of the molecular sensitivity in PET imaging has long been discussed with respect to imaging instrumentation and algorithms for data treatment.7 Geometrical collimation of γ-rays8 or replacement of γ-ray detectors with high purity Ge detectors9 improves the spatial resolution. Both of these techniques, however, reduce the detection efficiency of γ-ray photons and enhance statistical fluctuations, reducing the molecular sensitivity in PET imaging. Use of smoothing treatments for improving statistical fluctuations, on the contrary, deteriorates the spatial resolution.10 In this study, the molecular sensitivity in PET imaging is explored by means of 2-dimensional (2D) coincident measurements of γ ray photons from two-photon annihilation. A method for enhancing molecular sensitivity in PET imaging based on the quantum correlation of γ ray photons is proposed. II. PRINCIPLE OF PET IMAGING WITH QUANTUM CORRELATION OF γ RAY PHOTONS
In PET imaging, the energies of the two annihilation γray photons emitted at 180◦ are measured in coincidence by two intrinsic γ-ray detectors.4 The energies of the two γ-ray
86, 054301-1
© 2015 AIP Publishing LLC
054301-2
K. Sato and Y. Kobayashi
Rev. Sci. Instrum. 86, 054301 (2015)
FIG. 1. X-Y 2D presentation of energy resolution with a diameter of δ E (green circle), a box-shaped energy window with a side of δ E (blue square), and an additional box-shaped energy window with a side of δ E (red square) introduced by the quantum correlation of the coincidently measured γ-ray photons following Eqs. (5) and (6). The center corresponds to (511, 511) in the X-Y coordinate. The black solid and dotted lines correspond to E 1 + E 2 = 2m 0c 2 and E 1 − E 2 = 0, respectively. FIG. 2. Schematic diagram of the present experimental setup.
photons E1 and E2 are described as E1 = m0c2 + δE,
(1)
E2 = m0c2 − δE,
(2)
where m0, c, and δE are rest mass of the electron, the velocity of light, and the energy resolution, respectively. Fig. 1 shows a 2D schematic representation of the energies of the two γray photons coincidently measured. In this representation, the energy resolution of the 2D system is described as a green circle with a diameter of δE centered at X = 511, Y = 511. This circle is referred to as the resolution circle hereafter. In conventional PET imaging, each of the two coincident γrays is independently energy selected, which corresponds to the selection of the events that fall in a box-shaped energy window with a side of δE (see the blue square). In this case, the events in the regions outside the resolution circle, indicated by gray triangles denoted as A in Fig. 1, are included in the valid events but they are likely false signals causing noise in PET images. To reduce the coincident events in the regions A, the following quantum correlation of two γ-ray photons is introduced in addition to the conventional coincidence method. Equations (1) and (2) yield the sum energy ΣE and difference energy ∆E as E = E1 + E2 = 2m0c2, (3) ∆E = E1 − E2 = 2δE.
(4)
Equation (3) indicates the straight line passing through the center of resolution circle (511, 511) with a gradient of −1 (see the black solid line in Fig. 1), whereas E1 − E2 = 0 available from Eq. (4) passes through (511, 511) with a gradient of 1 (see the black dotted line in Fig. 1). Here, a box-shaped energy window with a side of δE indicated by the red square is additionally set by introducing the quantum correlation of the coincidently measured γ-ray photons following Eqs. (5) and (6) below, √ √ 2 2 δE < E1 − E2 < δE, (5) − 2 2
√
√ 2 2 1022 − δE < E1 + E2 < 1022 + δE. (6) 2 2 The coincident events within an octagon-shape energy window are now energy-selected, instead of those in the blue square, which results in the elimination of the false coincident events in the regions A.
III. EXPERIMENTAL SETUP
Fig. 2 shows a schematic diagram of the present experimental setup. 511 keV γ rays emitted as a result of positron annihilation in the samples are detected by scintillators coupled with photomultiplier tubes (PMT1 and PMT2). Two scintillators of Bi4Ge3O12 (BGO) each with a diameter of 1 in. and a thickness of 1 in. were used. PMT1 and PMT2 were collinearly aligned to each other mimicking a real pair of γ ray detectors in a PET system. A 22Na positron emitter with a source strength of ∼10−1 MBq sealed in a thin foil of kapton was mounted in a sample-source-sample sandwich. Two identical discs of single-crystalline Al were employed as samples. Analog pulses from PMT1 and PMT2 were transferred to a 2D-multichannel analyzer (2D-MCA) with a built-in ADC through an amplifier (AMP). Pairs of correlated digital outputs within a coincident time of 300 ns were stored in random-access-memory and displayed as a 2D image, controlled by a personal computer (PC).
IV. RESULTS AND DISCUSSION
Fig. 3 shows a 2D X-Y presentation of the coincidently measured γ ray photons, in which the center of the circle is the peak arising from two-photon annihilation, thus corresponding to the X-Y coordinate (511, 511). The fingerprint-like images at lower energy regions perpendicular to the X (E1) and Y (E2) axes are caused by incomplete charge collection and Compton scattering. A box-shaped energy window with a
054301-3
K. Sato and Y. Kobayashi
FIG. 3. X-Y 2D presentation of two γ ray photons. The blue square-shaped energy window corresponds to the energy window of a conventional PET system and an additional energy window, introduced based on the quantum correlation between the two γ ray photons is shown with the red square. The center of these squares is the peak arising from two-photon annihilation, thus corresponding to an X-Y coordinate of (511, 511). The coincident counts are highest here at this center point.
Rev. Sci. Instrum. 86, 054301 (2015)
spectrum obtained by introducing the quantum correlation of coincidently measured γ ray photons is an order of magnitude higher than that in conventional PET, demonstrating that the present method is able to improve the molecular sensitivity of PET imaging. The background due to accidental and scattered coincident events in the 1D γ ray energy spectrum is efficiently reduced in the vicinity of the energy-box windows in comparison with that by collimation of γ-ray photons of ∼0.01%.8 It is furthermore noted that the sensitivity of positron images can be improved by simply introducing the energy correlation between the two γ-ray photons without any significant instrumental changes. In principle, the SNR and the detection efficiency in PET imaging have a trade-off relationship, i.e., an increase in one leads to a reduction in the other and vice versa. The performance characteristics of PET imaging are thus often examined by the noise equivalent count rate (NECR)11 given by N EC R =
T2 , T2 + R + S
(7)
side of 200 ch (0.6 keV/ch) drawn as a blue square corresponds to the energy window of a conventional PET system, and thus contains false coincident events in the regions outside the resolution circles. Following Eqs. (5) and (6), a box-shaped energy window with a side of 200 ch was additionally set at the center of the resolution circle (511, 511), as drawn as a red square. This box-shaped energy window (rotated by π/4 compared to the conventional energy window) corresponds to an additional energy window based on the quantum correlation of the coincidently measured γ ray photons, i.e., the sum and difference of energies of the two photons. Fig. 4 shows (a) the projected 1D γ ray energy spectrum onto x-axis in the conventional (blue) box-shaped energy window and (b) that onto the diagonal-axis in the octagon-shaped energy window formed by the combination of both (blue and red) box-shaped windows. The projected energy spectrum onto the x-axis in the box-shaped energy window and that onto diagonal-axis in the octagon-shaped energy window correspond to conventional and present PET, respectively. Obviously, the SNR in the 1D γ ray energy
where T, R, and S are the true, random (accidental), and scattered coincidence count rates, respectively. As mentioned above, the present method based on the quantum correlation of γ ray photons sufficiently reduces the background due to random (R) and scattered (S) coincident events (see Fig. 4). From Eq. (7), it is seen that the value of NECR thus increases, demonstrating an improvement of the present system with respect both to the SNR and the detection efficiency. Generally, PET imaging in clinical and in-vivo small animal research is performed by employing a strong positron source more than ∼103 MBq with a short half-life in order to avoid excessive radiation exposure to the subject.12 The background level arising from random (R) and scattered (S) coincident events could be higher than that with the positron source of ∼10−1 MBq demonstrated here. A further improvement of both the SNR and the NECR is thus expected for the present system in real clinical and in-vivo environments. It is noted that enhancing the molecular sensitivity is a subject of interest in any PET imaging system, including time-of-flight (TOF)-PET13 and depth-of-interaction (DOI)PET.14 The TOF-PET technique requires fast scintillators such as, e.g., Lu2SiO5:Ce (LSO) and BaF2 with a fast decay time for achieving excellent time resolution. We have already succeeded in applying the proposed method for the PET imaging system with BaF2 scintillators.15 In addition, the present method can be utilized for PET imaging systems with different detectors such as high purity Ge detectors, which have been used to improve the spatial resolution down to 1 mm.9 We propose that the present method based on the quantum correlation of γ ray photons is not only simple but also universally applicable for any PET imaging system with different scintillators, detectors, application specific integrated circuits (ASICs), and so on.
FIG. 4. (a) Projected energy spectra into the x-axis (black solid line) and (b) the diagonal-axis (red solid line) in the box energy windows. The projected energy spectra into x-axis and diagonal-axis in the box energy windows correspond to conventional and present PET, respectively.
V. CONCLUSIONS
Molecular sensitivity in PET imaging was studied by 2D coincident measurements of positron annihilation 511 keV
054301-4
K. Sato and Y. Kobayashi
γ ray photons resultant from two photon annihilation. By introducing constraints based on the quantum correlation of the coincidently measured γ ray photons, i.e., the sum and difference energies of the photons, a box-shaped energy window, which is rotated by π/4 from conventional window, was additionally set around the peak center (511, 511) in addition to the conventional window. This reduces the noise originating from the false coincident events in the regions outside the resolution circle, by leading to an increase in the SNR by an order of magnitude compared to a conventional system. The improvement of performance characteristic in the PET imaging system was further demonstrated by an increase in the NECR, a metric which takes account of both the SNR and the detection efficiency. ACKNOWLEDGMENTS
We are grateful to Dr. Brian E. O’Rourke of the National Institute of Advanced Industrial Science and Technology for proof-reading the manuscript. This work was partially supported by a Grant-in-Aid of the Japanese Ministry of
Rev. Sci. Instrum. 86, 054301 (2015)
Education, Science, Sports and Culture (Grant Nos. 21540317 and 23740234). 1S.
S. Gambhir, Nat. Rev. Cancer 2, 683 (2002). W. Miller, N. J. Long, R. Vilar, and A. D. Gee, Angew. Chem., Int. Ed. 47, 8998 (2008). 3M. D. Harpen, Med. Phys. 31, 57 (2004). 4Positron Emission Tomography: Basic Sciences, edited by D. L. Bailey, D. W. Townsend, P. E. Valk, and M. N. Maisey (Springer-Verlag, London, Limited, 2005). 5C. S. Levin, Proc. IEEE 96, 439 (2008). 6A. K. Shukla and J. Utham kumar, Med. Phys. 31, 13 (2006). 7H. Peng and C. S. Levin, Curr. Pharm. Biotechnol. 11, 555 (2010). 8A. Rahmim and H. Zaidi, Nucl. Med. Commun. 29, 193 (2008). 9K. Ishii, Y. Kikuchi, S. Matsuyama, Y. Kanai, K. Kotani, T. Ito, H. Yamazaki, Y. Funaki, R. Iwata, M. Itoh, K. Yanai, J. Hatazawa, N. Itoh, N. Tanizaki, D. Amano, M. Yamada, and T. Yamaguchi, Nucl. Instrum. Methods Phys. Res., Sect. A 576, 435 (2007). 10A. M. Alessioa and P. E. Kinahan, Med. Phys. 33, 4095 (2006). 11S. C. Strother, M. E. Casey, and E. J. Hoffman, IEEE Trans. Nucl. Sci. 37, 783 (1990). 12C. G. Rhodes and J. M. B. Hughes, Eur. Respir. J. 8, 1001 (1995). 13K. Ishii, H. Orihara, T. Matsuzawa, D. M. Binkley, and R. Nutt, Rev. Sci. Instrum. 61, 3755 (1990). 14M. Soret, S. L. Bacharach, and I. Buvat, J. Nucl. Med. 48, 932 (2007). 15K. Sato and Y. Kobayashi, Japanese patent 4997603 (2012). 2P.
Review of Scientific Instruments is copyrighted by AIP Publishing LLC (AIP). Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. For more information, see http://publishing.aip.org/authors/rights-and-permissions.
