Simultaneous multi-nuclide imaging via double-photon coincidence method with parallel hole collimators

Multi-tracer imaging can provide useful information in the definitive diagnosis and research of medical, biological, and pharmaceutical sciences. Single-photon emission computed tomography (SPECT) is one of the nuclear medicine imaging modalities widely used for diagnosis or medical research and has a multi-tracer imaging capability. One of the drawbacks of multi-tracer imaging is crosstalk from other gamma rays, which affects the reconstructed image. Scattering correction methods, such as the dual- and triple-energy window methods, are used for conventional SPECT imaging to reduce the background caused by the crosstalk. This study proposes another crosstalk reduction method. Some nuclides emit two or more gamma rays through intermediate levels. Thus, detecting these gamma rays with the coincidence method allows us to distinguish a true gamma ray signal and a background signal. The nuclide position can be estimated at the intersection of two gamma rays using collimators. We demonstrate herein simultaneous 111In and 177Lu imaging via the double-photon coincidence method using GAGG detectors and parallel hole collimators. The double-photon coincidence method greatly reduces the background caused by other gamma rays and offers higher-quality images than does conventional imaging.

recently developed and can offer high-quality images because the energy resolution of CZT detectors is higher than that of scintillator detectors [19][20][21] . A high-energy resolution SPECT scanner can discriminate close energy peaks and reduce the crosstalk by a narrower energy window. Other approaches are scatter correction methods, such as the dual-energy window 22,23 and triple-energy window 24,25 subtraction methods.
This study proposes a novel method using coincidence detection to reduce crosstalk and distinguish nuclides. Some nuclides emit two or more successive gamma rays, which are called cascade gamma-rays, through intermediate levels of atomic nucleus via nuclear spin. Thus, similar to PET imaging, which detects coincidence events of annihilation gamma rays, the background signals can be reduced to random events within a time window using coincidence detection and energy selection. Moreover, since there is the time and space correlation between the emission directions of cascade gamma-rays, the probability distribution of the nuclide with coincidence detection can be limited to the intersection of each distribution obtained by single-photon detection if the imaging system can determine the direction of incoming gamma-rays. Figure 1a show the conceptual schematic of the doublephoton coincidence imaging we proposed in this paper, which utilizes the correlation of cascade gamma-rays originated from one atomic nucleus. A nuclide emits cascade gamma-rays ( γ 1 and γ 2 ) with energies of E 1    www.nature.com/scientificreports/ x, detection time t, and direction s (unit vector). When the cascade gamma-rays are detected with detector1 and detector2, the value of an image voxel p ′ i to add is ideally like below: where p ′ i is the position of the voxel and i is the index corresponding to the image voxel number ( i = 0,1, 2, . . . , N) . The correlated photons can be extracted by the coincidence detection of γ 1 and γ 2 within a time window. When the time resolution of system is faster than the half-life τ , the delay caused by the half-life can be measured in the spectrum of time difference.
For example, 134 Cs mainly emits 796 and 605 keV gamma rays through the intermediate level with a 5.12 ps duration. We have already applied the double-photon coincidence method to Compton imaging and demonstrated its effectiveness in improving the signal-to-background ratio (SBR) by using the intersection of double Compton cones 26,27 . The Compton imaging results of 134 Cs in the 137 Cs background in Ref. 27 showed the crosstalk reduction capability of the double-photon coincidence method. This method can also be applied to radionuclide imaging using a Pb-based collimator. The direction of incoming gamma rays is determined through mechanical collimation; thus, the coincidence detection of two photons can estimate the nuclide position in these intersection points. We have already demonstrated 111 In imaging using two GAGG pixel detectors equipped with parallel hole collimators. The 111 In position was correctly imaged by detecting coincidence events of 90°2 8 . 111 In is used for SPECT imaging and emits 171 and 245 keV gamma rays through the intermediate level with 85 ns duration (Fig. 1b). Its half-life is approximately 2.8 days. In these previous study [26][27][28] , the double photon coincidence method was applied to imaging only one double-photon emitter even though this method also has the potential to distinguish multiple double-photon emitting nuclides. Recently, we realized that a nuclide of 177 Lu, which is used for treating neuroendocrine tumors [29][30][31] , was another double-photon emitter in nuclear medicine. 177 Lu emits 208 and 113 keV gamma rays through the intermediate level with 0.506 ns duration after beta minus decay (Fig. 1c) 32 . Its half-life is approximately 6.65 days. The gamma rays from 177 Lu are suited for SPECT imaging; thus, the 111 In and 177 Lu combination is also used for dual-isotope imaging as a tool in the molecular imaging tracer design 15 . We demonstrate herein the multiple double-photon emitting nuclides imaging of 111 In and 177 Lu via the double photon coincidence method for the first time by using four 8 × 8 array GAGG detectors equipped with 8 × 8 array parallel hole collimators in order to show the capability to distinguish nuclides and the effectiveness of the double-photon coincidence method for crosstalk reduction and SBR improvement.

Results
Simultaneous 111 In and 177 Lu imaging in microtubes. Figure  In this study, this artifact is not essential and can be solved by improving the experiment environment. Table 1 presents the SBRs in the images and the absolute detection efficiencies of Camera 1 in the ROI shown in Fig. 2a-3, b-3. Although the detection efficiencies of double-photon coincidence imaging decreased by approximately 10 −4 times compared with those of single-photon imaging, the SBRs in the double-photon images increased by approximately two or more times (Table 1). Figure 3 shows the results of three-dimensional (3D) imaging with four cameras. Specifically, Fig. 3a-4, a-5, b-4 and b-5 depict the 2D slice images in the x-y plane by the back projection (BP) method using single photons. Reconstruction methods, such as the filtered back projection and maximum likelihood-expectation maximization methods, were not applied herein; thus, intersection lines are drawn in single-photon images. Similar to 2D imaging in one direction, the artifacts caused by the background events from another nuclide can also be observed in (a-5), (b-4), and (b-5). By contrast, double-photon coincidence imaging can determine the RI source position at one voxel by taking the coincidence events at 90°. Figure 3a-3,b-3 illustrate the 2D slice images in the x-y plane of 111 In and 177 Lu by the double-photon coincidence method. Each position was correctly visualized. The 2D slice images in the x-z and y-z planes were also correctly obtained ( Fig. 3a-1,a-2,b-1,b-2). Although the detection efficiencies of double-photon imaging were 10 4 times smaller than those of single-photon imaging, the SBRs of the x-and y-axis of the x-y plane images were evaluated from the 1D plots in the x-and y-axis and found to greatly increase when the double-photon coincidence method was used ( Table 2). The SBRs of the y-axis on the double-photon images were remarkably larger than those of the x-axis because the RI sources were placed along the x-axis, and some of the background in the ROI of another nuclide was not eliminated.  Figure 4 shows the 3D images of the 111 In and 177 Lu distribution sources. 111 InCl 3 was in an acrylic case of the alphabetical letter "T", whereas 177 LuCl 3 was in an acrylic case of the alphabetical letter "U". The double-photon images in Fig. 4a-2,b-2 are clearly visualized without any rotation and reconstruction methods compared with the single-photon images in Fig. 4a-1,b-1. Although the detection sensitivities depending on voxels were not considered in this study, the sensitivity correction will improve the images of the distribution sources. In the single-photon image of 208 keV gamma rays from 177 Lu ( Fig. 4(b-1)), the background caused by 111 In strongly contributed to the artifacts compared with that of the experiment using microtubes because the photopeaks of this experiment shifted from those of the calibration data due to the change of the gain of silicon photomultipliers (SiPMs) caused by the change of the environment temperature. This background was greatly reduced by the double coincidence method. The low intensity voxels in the alphabetical letter "U" were due to inhomogeneity of 177 Lu solution volume. However, the artifacts were still seen in the double-photon image of 177 Lu (Fig. 4b-2). More background can be reduced by implementing a temperature compensation circuit or by using a constant temperature chamber.

Discussion
We demonstrate herein simultaneous 111 In and 177 Lu double-photon coincidence imaging with an 8 × 8 array of parallel hole collimators. 111 In and 177 Lu, which are used in nuclear medicine, are double-photon emitters. 111 In emits 171 and 245 keV gamma rays, whereas 177 Lu emits 113 and 208 keV gamma rays. The energies of these gamma rays are close; thus, the crosstalk between the nuclides, including the overlaps in the spectra and scattering events, strongly affects the artifacts in the images with the system of ~ 12% energy resolution at 245 keV. Although the absolute detection efficiencies of double-photon imaging were 10 4 smaller than those of single-photon imaging, the crosstalk was greatly reduced by double-photon coincidence imaging for both sources in the microtubes and distribution sources. However, some of the background was not eliminated. One of the causes is the shift of the peak positions caused by the changes in the SiPM gain due to the change of the environment temperature, especially for the long measurement experiment using the distribution sources. The energy windows were selected from the calibration data measured without a collimator; thus, the shift of the peak positions contributed to the background and resulted in incorrect coincidence events. Generally, the gain of SiPM increases as the temperature decreases 33 . The peak positions of 113, 171, 208, and 245 keV gamma-rays in the spectra of the measurement of distribution sources were shifted approximately 7.5% higher on average. The measurement of distribution sources was conducted during the night, thus, it was assumed that the temperature was lower than that in the measurement of calibration data. With the shift of peak positions, the overlap range in the time width window, which is corresponding to the energy window, of 208 keV gamma-ray with those of 171  www.nature.com/scientificreports/ and 245 keV gamma-rays was increased from 47.4 to 55.2%. Thus, the background of 111 In appears in the singlephoton image of the 177 Lu distribution source ( Fig. 4a-1) more than that of the micro tube ( Fig. 3b-5). On the other hand, there was no overlap range in the 113 keV time width window with that of 171 keV gamma-ray, thus, incorrect events in the 113 keV window were just only scattering events of higher energies gamma-rays. While the detection probability of the incorrect event directly affects the background in the single-photon image, that of double photon coincidence method is greatly decreased because it is estimated as the product of the detection probabilities of the incorrect event in energy windows of gamma1 and gamma2. The peak shift will be solved by implementing a temperature compensation circuit or by using a constant temperature chamber. Another cause is the chance coincidence events within the time windows. The approximate ratios of the chance coincidence events to the coincidence events within the time windows are 35.4 ± 1.87% ( 111 In) and 36.3 ± 2.56% ( 177 Lu), which were calculated from the time difference histogram (Fig. 6c). Although it is impossible to completely eliminate the chance coincidence events, the time resolution improvement can reduce them. In this study, the sensitivity correction was not applied for imaging. The single-photon efficiency is inversely proportional to the square of the distance between a source position and a detector. Hence, the double-photon coincidence detection efficiency in a voxel is the product of detection efficiencies of the two detectors. The sensitivity correction of each voxel for the double photon coincidence imaging should be one of future works. There is room for improvement in terms of the time resolution of the detector system, experiment environment, and sensitivity correction, resulting in a higher-quality image. In summary, the double-photon coincidence method is effective for multi-nuclide imaging to reduce the crosstalk between nuclides and distinguish them. Although the detection sensitivity of this method is significantly reduced compared with that of single-photon imaging, a higher-quality image can be offered without any rotation and reconstruction method by taking coincidence events, except at 180°. Recently, a new concept of the collimation method, which uses a scintillator detector as a collimator was proposed. For example, an active pinhole camera, which consists of a scintillator detector that has a pinhole and a non-hole detector, was reported 34 . The detection sensitivity of the double photon coincidence method with collimators we proposed in this paper can be improved by combing the new collimation method since the active collimator can detect gamma-rays.
The characteristics of a GAGG scintillator are desirable energy resolution (4% with an avalanche photodiode [APD]), high light yield (56,000 photons/MeV), high density (6.63 g/cm 3 ), moderate timing resolution (150 ns), non-deliquescence, and non-self-irradiation. The 8 × 8 array of HR-GAGG scintillators with a pixel size of www.nature.com/scientificreports/ 2.5 mm × 2.5 mm × 4 mm was used as the pixel detectors. The pitch size was 3.2 mm × 3.2 mm. Each crystal was separated by BaSO 4 reflectors that can improve the light output compared with that with a Teflon tape or an enhanced specular reflector film 36 . As a sensor for scintillation light detection, the 8 × 8 array of SiPMs (Hamamatsu MPPC S13361-3050) was coupled with the HR-GAGG arrays and wrapped with Teflon tapes. The pitch size of the SiPM array was similar to that of the HR-GAGG array. For mechanical collimation, an 8 × 8 array of a Pb-based parallel hole collimator was equipped with an HR-GAGG pixel detector, with a hole diameter of 2 mm. The collimator thickness and pitch size were 15 mm and 3.2 mm × 3.2 mm, respectively, corresponding to those of the pixel detector.
Signal processing and data acquisition system. The charge signals from the SiPMs were processed using the dynamic time-over-threshold (dToT) method 37,38 . The dToT method converted analog signals corresponding to the energy of gamma rays to digital signals as a time width via a comparator. Compared with the conventional signal processing method using analog-to-digital converters for pulse height measurements, the dToT method can offer lower power consumption and circuit simplicity. Thus, it was suited for multi-channel parallel signal processing. Moreover, the linearity between the time width and the radiation energy was improved by using a dynamic threshold instead of a static threshold used for the conventional ToT method [39][40][41] . A signal processing board comprised 64 channels of dToT-based circuits comprising an amplifier, a dynamic threshold generator, and a comparator. The intrinsic time resolution was approximately 50 ns (full width at half maximum (FWHM)). The ToT outputs were transferred to a 144-channel field-programmable gate array (FPGA, Xilinx Artix7)-based data acquisition (DAQ) system 42 through KEL coaxial cables. The FPGA on the DAQ board operated with a clock of 500 MHz. The digital signal (T0 signal) with time information was also input to the DAQs and sent to a computer as the time data at every 1 ms interval after being processed by FPGA to synchronize the time-of-event data generated by two or more DAQs offline. Besides the time data, the event data comprising the time of flight (TOF) between the rising edge of a T0 signal and the falling edge of a ToT signal, channel number, and time width were also sent as the list mode data to the computer through the local area network. In the analysis, the time-of-event data were calculated using the time data, TOF, and time width to extract the coincidence events.
Experimental setup. Figure 5 shows the experimental setup. Four gamma cameras were placed at 90°. Analysis and event selection. Figure 6a illustrates the spectra of 111 In and 177 Lu obtained with 1 px of an HR-GAGG pixel detector. The average energy resolutions of 256 px were approximately 17.6% (FWHM) at 113 keV, 12.2% (FWHM) at 171 keV, 11.6% (FWHM) at 208 keV, and 12.0% (FWHM) at 245 keV. The energy resolution at 245 keV decreased because of the non-linearity caused by the limit of the dynamic range of the CMOS amplifier on the dToT board. Overlaps existed between the photopeaks of 171, 208, and 245 keV. The photo-absorption events of 171, 245 (from 111 In), 113, and 208 keV (from 177 Lu) gamma rays were extracted for imaging, which were within the time width window similar to that shown in Fig. 6b. The time width window corresponding to the energy window was decided from the calibration spectra measured without collimators. These extracted photopeak events were used for single-photon imaging, whereas the coincidence events of the cascade gamma rays within a time window were used for double-photon imaging. The z-positions of the extracted coincidence events were equal. Figure 6c shows the histograms of the time difference (171-245 keV for 111 In and 113-208 keV for 177 Lu) obtained from the experiment using microtubes. 111 In has a relatively long duration of 85 ns at the intermediate level after emitting 171 keV gamma rays; hence, a tail caused by the duration is shown in the time difference histogram. Conversely, a tail is not shown in the time difference histogram for 177 Lu because the 0.506 ns duration cannot be measured by our system with a 50 ns time resolution. Figure 6c indicates that the coincidence events of 111 In and 177 Lu were correctly detected. From these results, the time windows for 111 In and 177 Lu were from − 400 to 40 ns and from − 100 to 100 ns, respectively.
Imaging method. Figure 7 shows the imaging method used herein. Figure 7a,b show 2D imaging methods.
The photopeak events measured by Camera 1 were utilized for the single-photon 2D imaging in one direction (Fig. 7a). The coincidence events between cameras 1 and 2, 3, or 4 were used for double-photon coincidence 2D imaging (Fig. 7b). Two-dimensional imaging offers an image in the x-z plane with 8 × 8 px. An incremented pixel was determined by a detector position. In the double-photon coincidence 2D imaging, only the reduction of background was shown. Figures 7c,d show 3D imaging methods. The BP method was applied for the single-photon 3D imaging (Fig. 7c). We did not perform the measurement with rotations; thus, eight voxels in the x-y plane were incremented by 1/8 from two directions. By contrast, the coincidence events of 90° were used for double-photon 3D imaging because these can determine the RI source position at one voxel without any imaging reconstruction www.nature.com/scientificreports/  www.nature.com/scientificreports/ method and rotation (Fig. 7d). A voxel determined by an intersection of the coincidence event directions was increased by 1. This can be expressed using the Eq. (1) like below: where total p ′ i is the value of an image voxel, p ′ i is the coordinate of the image voxel with the index i corresponding the number of voxel, k is the index corresponding to the number of 90 • coincidence events ( k = 1, 2, . . . , M) . Then smoothing using the Gaussian function was performed for all images.

Calculation of SBR.
We evaluated the SBRs for 2D and 3D imaging of 111 In and 177 Lu in the microtubes. The SBR is defined as follows for the SBR evaluation of 2D imaging in one direction: where C ROI is the sum of the pixel values in the ROI (4 × 5 px) and C all is the sum of the pixel values in an image (8 × 8 px). Figure 2 presents the ROIs of the 111 In and 177 Lu images. The C all − C ROI value was defined as the background.
For 3D imaging, the SBRs in the x-and y-axis were evaluated from the 1D plots of the x-and y-axis in the x-y plane. A 1D plot was extracted from the x-y plane image, including the maximum value. Figure 2a-6,a-7 The coincidence events of 90° are used for double-photon 3D imaging. A voxel determined by an intersection of the coincidence event directions is increased by 1. This figure was created using the software (Adobe Illustrator, Illustrator CC 24, https:// www. adobe. com/ produ cts/ illus trator. html).