Evaluation of an instrument to improve PET timing alignment

Methods A timing alignment probe containing a plastic scintillator with an embedded sodium-22 source which is optically coupled to a fast photomultiplier tube (PMT) is described and tested. When a positron is ejected from the radioactive atom’s nucleus, its kinetic energy is absorbed in and can be detected as a light flash from the scintillator. This is used as the reference time for each atom’s positron decay. It is only after the positron slows that it can combine with an electron, forming positronium after which the 511 keV annihilation photons will be created, possibly traveling to the PET detectors. In practice, the probe is placed in the center of the scanner’s field of view and connected to the coincidence circuit. Since the delay between an annihilation photon’s detection and positron detection is almost identical (the lifetime of positronium in a solid is extremely short, and the gamma rays’ path lengths are equal with the probe in the center of the scanner), the probe’s signal provides a fixed reference time to which the response of individual crystals in the PET detectors can be compared. We present an evaluation of the performance of this probe. We first investigated the intrinsic performance of the time-alignment probe comparing its timing resolution with two barium fluoride crystals in coincidence. We then investigated the timing performance of the probe in coincidence with various individual scintillation crystals and with detectors from two commercial PET scanners. Results The best full-width at half-maximum (FWHM) timing resolution of the probe was found when in coincidence with BaF 2 at 400 ps. The common commercial scintillator lutetium oxy-orthosilicate (LSO) was tested and its FWHM was 510 ps. When testing the crystal arrays used in two commercial block detectors it was found that there are significant, systematic timing delays among the crystals. In the Siemens HiRez ® detector the average time difference between the positron detection and annihilation photon detection is 500 ps with a standard deviation of 115 ps. In the Siemens Focus ® detector the average was 1000 ps and a standard deviation of 400 ps. The reasons for the variation in apparent arrival times among the crystals appear to be due to the electronic readout rather than light transport from the crystals to the PMT. Conclusion Many PET scanners use a global time offset for each detector, and these variations in apparent time delay from individual crystals in the detector would have a significant impact if these detectors were employed in a time-of-flight (ToF) PET scanner. Keywords Time alignment PET Calibration 1 Introduction A PET timing alignment probe, based on a patent by Thompson and Camborde [1] was previously described by our group [2] . The original version used a nominal 10 μCi (0.37 MBq) source and a 9 mm photomultiplier. Further testing by Moses and Thompson [3] and McElroy et al. [4] showed that it could be useful in providing more precise timing alignment than conventional techniques in prototype scanners. However, other tests at Siemens Molecular Imaging on commercial scanners (personal communication) showed that the activity in the central source produced fewer counts that the intrinsic activity in the detectors due to the presence of 176 Lu in scanners Lutetium oxy-orthosilicate (LSO) crystals. This made it difficult to correlate signals from the probe and detectors in order to estimate the time delays. Based on these results a new version with 10 times more activity and a faster PMT was developed. This new version has since been certified as a radiation emitting device by the Canadian Nuclear Safety Commission thus allowing it to be used without a license for the 3.7 MBq of 22 Na it contains. The concept would facilitate an improved and more convenient method of time alignment for PET scanners [1] . Consisting of a positron source embedded in a plastic scintillator, which is attached to a photomultiplier tube, the probe serves as a common reference clock, with respect to which the time of response of each crystal in each PET detector can be measured. Time alignment is a critical procedure needed for a properly functioning and efficient PET scanner. With the recent development and ongoing research into faster and more efficient scintillators, the development of more advanced scanners has followed. In these scanners, primarily ToF scanners, proper time alignment and event-time recording becomes integral to the operation of the scanner. In its simplest terms timing alignment is the ability of two detectors to report two temporally aligned detections as happening at the same time. If each detector has a photon interacting with it at the same time, then, through the path of the PMT and the electronics, the events should record an identical time stamp for the time of their interactions. Small deviations in the time stamp are inevitable as a consequence of imprecise timing information from the scintillator, PMTs and electronics, but systematic differences can be estimated and compensated for. Time alignment is the process used to minimize these systematic errors. One can think of timing alignment process as shown in Fig. 1 , which shows the coincidence counting response of two detectors to a source placed between them represented as a Gaussian curve. The vertical lines represent the scanner’s coincidence window. If one of the detectors reports the detector of a gamma ray in a manner which is systematically late or early (triangle curve in Fig. 1 ), this detector pair will record fewer true coincident counts. By performing repeated experiments with different timing offsets for each detector one can maximize the coincident count rate, and thus find the best time offset for each detector. The offset is an amount of time that is added to or subtracted from a signal to ensure the same time report from each detector. Doing this for each detector pair would be very time consuming, and is not practical for a large number of detectors in a PET scanner. The other problem is the adjustments to the time offset are done blindly since there is, initially, no indication whether there needs to be more or less offset or how much offset may be needed. Several other methods have been developed to perform the timing alignment of PET scanners to ensure that all detectors report the arrival time of gamma rays to the coincidence circuit and thus compensate for the various instrumental delays in the processing of individual detection channels. The most common method takes advantage of the radioactivity in the orbiting transmission source [5] . For example, this method is used to optimize the timing resolution of all the detectors of the CPS HRRT PET scanner to 2.82 ns, enabling the use of a 6 ns timing window [6] . Another method takes advantage of the intrinsic radioactivity embedded in LSO scintillators that are used in new high-speed PET scanners [7] . This is hampered by the low count rate of LSO, so it is not commonly used. Researchers at General Electric Medical Systems have reported procedures which are able to perform timing alignment in a closed loop fashion [8] , allowing the timing alignment process to converge more rapidly than previous methods. This technique is the subject of US patent issued in 2005 [9] . This technique allows the measurement of block-to-block timing differences but also estimates the individual time differences within the blocks of crystals. The authors point out that they measure the time differences between recorded events using this technique not the absolute time taken from a common reference source. This requires an iterative process which is said to converge rapidly requiring only three iterations. Another group [10] , recognizing the benefits of a central source for timing alignment, places a centrally positioned source in a small steel cylinder which causes some of the 511 keV gamma rays to scatter allowing those which scatter though small angles to remain in the scanner’s photo-peak energy window, but spread enough so that a small array containing several diagonally opposite crystals to appear in coincidence, even though the pairs of crystals are not precisely collinear with the source. They have successfully used this to perform the timing alignment of a ToF PET scanner. This method still requires iterations to determine whether the crystals are early or late, since there is no common time reference. In conventional PET scanners the quality of the time alignment has the effect of reducing noise and improving image quality in the PET image. The reason for the improvement is the reduction in the ratio of random counts to the true counts in the image. Random counts are the result of a recorded annihilation being the result of the detection of one photon from two separate annihilations. The number of random counts is proportional to the width of the coincidence timing window: the time gap allowed between the detection of two events in order for them to be considered to originate from one annihilation. The coincidence timing window can be reduced without a great reduction in the number of counts with good time alignment; however if the timing is misaligned (as in Fig. 1 ), there will be fewer true coincident counts, but the random count rate will not change. The count rate for randoms is [11] R ̇ i j = 2 τ C ̇ i C ̇ j where C i and C j are the individual single count rates for two detectors in coincidence and τ is the width of the timing coincidence window. 2 Materials and methods The time alignment probe that our group developed consists of a plastic scintillator optically attached to a fast PMT. The scintillator is machined into a cylinder with a small cavity in the center. The cavity has been filled with 3.7 MBq of activity from positron emitting 22 Na ( Fig. 2 ). The scintillator and PMT are capped with a black plastic cover in order to provide a light seal. When each sodium atom decays a positron is emitted. This positron’s kinetic energy is absorbed in the plastic scintillator and is converted into a light flash, which is detected by the PMT and converted to an electrical signal. The positron annihilates in the plastic creating two photons, each with an energy of 511 keV. Either or both of these photons may be detected by the scanner’s detectors. The time stamp from each detector in the PET scanner may now be aligned with the time of the detection of the positron from the probe and its single detector and thus a unique reference time is obtained, something that is lacking in other alignment methods. The plastic scintillator is polyvinyl toluene [12] and the PMT is a Hamamatsu H6610 ( λ min =160 nm, λ max =650 nm, λ peak =420 nm, 160 ps transit time spread, Fig. 3 ) [13] . This PMT was selected for its low transit time spread (TTS) and because it has a synthetic silica window, enabling the use of BaF 2 crystals, which emit in the UV spectrum. A lower cost PMT, which possesses the same time characteristics, but lacks the silica window, is also available. A series of experiments was performed to evaluate the timing probe and the timing resolution of a variety of individual scintillation crystals, and two commercial PET detectors. Pairs of sample crystals: BaF 2 , LYSO and LaBr 3 were obtained from Saint Gobain Crystals. The LSO crystal was provided by Siemens Molecular Imaging and the plastic scintillator from Alpha Spectra. Most were right circular cylinders whose dimensions are given in Table 1 . In addition, two commercial PET detectors blocks: a HiRez ® detector and Focus ® Micro-PET both provided by Siemens Molecular Imaging detector were tested. The HiRez detector has a 13×13 matrix of LSO crystals coupled to four cylindrical PMTs. The Focus ® detector has a 12×12 matrix of LSO crystals coupled to a Hamamatsu position-sensitive PMT. When measuring the timing characteristics of individual crystals they were attached to the same Hamamatsu H6610 PMT. Individual crystals were tested by optically coupling them to the PMT and light sealing them; they were then placed in coincidence with the timing probe (with one exception). The output from each PMT was connected to one of the inputs of a Canberra 454 constant fraction discriminator (CFD) [14] . The outputs of the CFD were connected to the “start” and “stop” inputs of a Canberra 2145 time to amplitude converter (TAC) [15] . The “stop” signal is routed through a Canberra 2058 switchable delay box before being sent to the TAC. This is done to ensure a positive TAC signal in all cases, and the addition of a small delay in measurements provides twin peaks in order to calibrate the time spectrum in channels per nanosecond. When a commercial PET detector was tested, the PMTs from that PET detector were used. The setup for the testing of a commercial PET block detector is more complicated, but fundamentally similar. A non-commercial nuclear instrument module (NIM) sums the four signals from the PET detector to produce a single fast timing signal for input to a CFD and individual integrated signals ready for sampling by a Jorway Aurora 14 six channel ADC. Another channel of the ADC receives the time delay output from the TAC. The ADC is readout by a Compac Alpha workstation to which the ADC is interfaced via its SCSI bus. The acquisition software can save a “list-mode” file for later analysis with different energy windows or time calibration, and can also build images during acquisition using preset time and energy windows. Individual energy gains can be applied to each crystal as is normally required in conventional PET detectors. The software thus allows an energy window to be applied so that only events within 511 keV will be included. The display and analysis software uses an algorithm appropriate to the detector under evaluation to encode the position the detection of each gamma ray in a 256×256 matrix. This allows each crystal in the detector to be visualized as in a conventional PET detector. Sixty-four of these matrices are assigned to time delays according to an adjustable calibration factor. The individual crystal identification matrices are displayed in raster format as shown in Fig. 4 . The top left image contains the sum of all others and so appears like the conventional PET detector crystal identification matrix. The image just to the right of the sum image shows those detections when there was no timing signal from the TAC due to the TAC’s intrinsic dead time, or the timing signal was smaller than set up for this experiment. This will also occur either when the positron is not detected due to its energy being below the probe’s threshold, but a gamma ray from the probe is detected, or when the intrinsic activity from the 176 Lu causes the detector to trigger. The image in the bottom right corner shows those gamma rays which were detected beyond the time range selected in that study. These may be due to random counts, or result from a very narrow time range. These “too early” and “too late” images are very useful in setting up the timing study. From the time analysis it can be seen if there is a crystal or set of crystals that arrives chronically early or late. By way of example, the data shown in Fig. 4 were acquired with a shorter cable connecting the lower right PMT of the detector so gamma rays detected by crystals closest to the lower right PMT appear to arrive earlier than those from the rest of the block. The number of counts required to generate a timing spectrum depends on the timing accuracy required, the efficiency of the probe in detecting positrons, the solid angle subtended by the crystal and its detector efficiency for 511 keV gamma rays. From a review of the recent PET scanner performance literature, the table presented in Fig. 5 shows the expected count rate for each crystal in a variety of well-known PET scanners based on the timing probe’s measured efficiency of 50% positron detection. The timing spectrum for the Focus ® detector was collected for ten individual 1 min scans in order to estimate the accuracy of this timing method. The time offset for the crystals was then averaged and the standard deviation calculated. 3 Results In order to provide an ideal time resolution, we attached BaF 2 to two PMTs and placed a source between them. Since BaF 2 is the fastest scintillator presently available, this would give a value to which the timing resolution of the other crystals can be compared. Since the plastic scintillator is slower than BaF 2 (2.5 ns vs. 0.6–0.8 ns), none of the results with the timing probe is expected to be better than the minimum resolution set in the BaF 2 –BaF 2 experiments ( Table 1 ). In current practice, the most commercially relevant scintillators tested were the individual LSO crystal and the two LSO crystal blocks (HiRez ® and Focus ® detectors). Their importance is due to being the most common scintillators in modern commercial PET scanners and the crystal of choice in time-of-flight PET scanners. The setup of the tests for the block detectors was designed to mimic what is done in a complete PET scanner. The goal was to see the block-wide differences in time resolution that can be seen amongst the crystal matrix and the PMT(s). Both of the block detectors had a set of LSO crystals as the scintillator, but employed different PMT technologies. The HiRez ® detector has a set of four PMTs attached to the crystal block and used Anger logic to position the event in the crystal. The Focus ® detector used a single position-sensitive PMT (PSPMT) with a resistor chain readout to place the event. Fig. 6 shows the raw display of the arrival time distribution in the HiRez detector. The frame-to-frame difference is 250 ps. The analysis software allows individual crystals in the matrix to be identified and the time dispersion can be fitted to a sum of three Gaussian functions. The FWHM and FWTM along with the centroid (representing the average arrival time) can be measured. The arrival times are plotted as a bar-graph and shown in Fig. 7 and the FWHM time resolution in Fig. 8 . The analysis of the time resolution of the individual crystals in the block reveals the advantage that would be had if the alignment were performed on a crystal by crystal basis ( Fig. 5 ). In the HiRez ® detector the signals from two of the corners arrive to the electronics much earlier (the short bars, Fig. 7 ) then those of the other two corners (the long bars, Fig. 7 ). The fastest crystal had the events detected 252 ps after the probe detected the positrons; the slowest was 781 ps after the probe. The average is 495 ps with a standard deviation of 114 ps. In the Focus ® detector there is a very different pattern apparent in the arrival time crystal map ( Fig. 9 ). The events in the center of the crystal block are reported at a much latter time than those from the edge crystals ( Fig. 10 ). The maximum and minimum differences are 1.648 and 0.281 ns, with an average difference of 1.02 ns and a standard deviation of 0.39 ns. If these detectors were used in a time-of-flight PET scanner, which uses the time of arrival difference between the annihilation photons, a difference of 1.4 ns would result in an event misplacement of 20.5 cm, which is completely unacceptable. The FWHM time resolution of the individual crystals is seen in Fig. 11 . When ten 1 min scans were performed, the standard deviation in the delay between the trigger pulse and a single crystal’s response was 71 ps. 4 Discussion Our evaluation of the Scanwell Systems timing alignment probe with various scintillation crystals demonstrates that the plastic scintillator is not as fast as the BaF 2 crystal. Comparing the timing resolutions presented in Table 1 shows that it is comparable with LaBr 3 , and better than LSO. The principal application of this device is in the alignment of all the crystals in a complete PET scanner. This was not possible in this study since none of the scanners available had an input to which the probe could be connected. The main attraction of this concept compared with other techniques for time alignment is that none of the other techniques can use a common reference. In order to have a valid coincidence between detectors in a normal PET scanner, the source must be on the line joining the two detectors. If the source were in the center, only diametrically opposed detectors can be aligned to each other. If the source is moved away from the center, ToF delays are introduced. If the source used for transmission scanning is employed, these ToF delays are quite significant. (∼4 ns). The probe used here detects positron decay rather than one of the collinear gamma rays resulting from positron annihilation. Thus it no longer needs to be on the line joining two detectors. Placing the source in the center of the scanner eliminates ToF delays. Furthermore, having one unique signal with which to align all the crystals allows the collection of a complete set of time delay spectra from each crystal (with respect to the probe’s signals) simultaneously. This enables the possibility of a single pass time alignment. The count rates in each crystal for various PET scanners show a wide variation according to the crystal size and ring radius. If one considers those scanners which can operate in the time-of-flight mode, the Siemens “HiRez” and the Philips “Gemini TF” single crystal count rates of about 30 cps are possible. In a study to estimate the error expected in the timing offset as determined from ten 1 min measurements with the Focus ® detector the standard deviation was found to be 70 ps. A detector from the Gemini scanner was not available to test. In a traditional block detector, an array of scintillating crystals is attached to four PMTs. The ratio of the amount of light reaching each PMT is used to calculate the position of each photon’s detection in the scintillator. In order to enable this function, each PMT in the block must output the same signal amplitude for the same input light. This is done by adjusting the gain of each PMT in the block. Adjusting the gain essentially changes the voltage applied across the dynodes in a single PMT. Reducing the voltage reduces the energy of the electrons released from each dynode, so that when they strike the next dynode, fewer secondary electrons are liberated. However, reducing the electrons’ energy to change the gain implies that they travel more slowly. For example, in a series of four PMTs, with 1200 V applied to the block, the individual voltages could be 1150, 1200, 1225 and 1250 V so that each PMT has a matched output. While adjusting the gain works well making the amplitude of the PMT outputs same, the time taken by the PMT to convert light to an electrical signal will no longer be consistent. This property of PMTs is known as the transit time. The transit time given by a PMT manufacturer is usually given at or beyond the maximum voltage rating. For example, the Photonis XP1452 PMT used in some PET scanners has a transit time of about 34 ns. Using the parameters of these PMTs, Fig. 12 shows the effect of relatively small voltage changes on their transit time. From the number of dynodes n d , the distance between each dynode, D d and the applied voltage, V , one can estimate the total transit time in a PMT as a function of applied voltage. t cathode − anode = 2 D d ( n d + 1 ) / 2 e V / m ( n d + 1 ) A plot of this function is given in Fig. 11 . A voltage adjustment of 50 V can make a difference of about half a nanosecond. This difference will cause a relatively large inconsistency in the arrival time in the entire block detector. If each crystal were aligned to a common reference this difference could be compensated for and the output matching would also be successful. The construction of the Siemens Focus ® detector is different. Other than a different number of crystals, the primary difference is that it employs a position-sensitive PMT. These PMTs have two orthogonal sets of anode wires the relative signal amplitudes on which provide positional information about the signal. In order to simplify the readout of these anodes, they are connected by a resistor network. However, each anode has a stray capacitance associated with its surrounding structure. We believe that the effect shown in Figs. 9 and 10 can be explained by considering the propagation of the signals from the anode which receives the peak signal to the ends of the inter-anode resistor network. We have written a simulation to show the output of each anode (and different position on the PMT face) for a given input signal. In Fig. 13 , the simulated output, shown normalized to the maximum, from each anode is shown. In this case, the signal is actually greatest on anode #1. The top line shows a fast rising signal with a realistic decay time of 40 ns. The other signals appear later and would have lower amplitudes. When these weighted signals are summed an early signal is seen from the end of the inter-anode resistor chain at anode 1, and a smaller delayed signal at the other end of the resistor chain. However, if the gamma ray is detected near the middle of the PMT the signals from both ends of the anode resistor chain are of equal amplitude, but would be delayed by the signal shown for anode 3. Since the temporal position of the peak is a very important factor in the time reporting in time pickoff electronics, it is clear from Fig. 13 that which anode the signal is on becomes an important factor. Once again, this problem could be solved by employing a crystal by crystal time offset to account for this. 5 Conclusions In testing the block detectors we were able to show that there are systematic time delays across each crystal matrix. For this reason there needs to be a system wide, crystal by crystal time alignment. Just as there is a need for an adapted energy window applied to each crystal, so should a separate time offset be applied rather than just one for each block. Advanced techniques such as time-of-flight require very accurate time stamps from the system in order to operate properly. On a conventional scanner, this is also very useful to decrease the system wide time resolution, which will decrease random counts and increase image quality. The time alignment probe we have developed and tested provides a superior method to perform time alignment due to its sufficiently high count rate and most importantly, its constant clock/frame of reference for each event in the PET scanner. As seen in the work by McElroy, the previous generation of the probe was used to improve the time resolution of their scanner from 16.5 to 10.2 ns [4] . System wide time-stamp values seen in the studies would result in time-of-flight errors as large as 20.5 cm, which is unacceptable. In a conventional scanner, the value to be considered in reducing random counts is also very advantageous as the number of random counts is linearly related to the width of the timing window. If properly aligned, which the timing probe can do accurately and less labour intensively, the timing window can be reduced leading to more efficient use of the detector data and higher-quality images. Our repeat study results suggest that a single 1 min scan would provide sufficient data to time-align every crystal in the scanner to an accuracy of 70 ps, which is probably a sufficient accuracy for even a ToF scanner. With this relatively fast procedure in place may be even desirable to incorporate such a scan into the daily quality control protocol used to optimize the scanner’s ToF performance for each day’s scanning. Acknowledgements This work was sponsored by Grant # OPG - 003672 from the Natural Science and Engineering Council of Canada to C.J. Thompson. The PET block detectors were provided by Siemens Molecular Imaging. Lissa Tegleman of Eckert and Ziegler prepared the sources used in these timing probes. References [1] C.J. Thompson, M. Camborde, Instrument and method to facilitate and improve the timing alignment of a PET scanner, US Patent 7247844, July 24, 2007. [2] C.J. Thompson M.L. Camborde M.E. Casey IEEE Trans. Nucl. Sci. NS-52 2005 1300 [3] W. Moses C. 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