Nuclear Instruments and Methods in Physics Research A

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1 Nuclear Instruments and Methods in Physics Research A 622 (2010) Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research A journal homepage: A simple and improved digital timing method for positron emission tomography Wei Hu a,b, Yong Choi a,b,n, Key Jo Hong a,b, Jihoon Kang a,b, Jin Ho Jung a,b, Youn Suk Huh a,b, Hyun Keong Lim a,b, Sang Su Kim a,b, Byung Jun Min a,b, Byung-Tae Kim b a Department of Electronic Engineering, Sogang University, 1 Shinsu-Dong, Mapo-Gu, Seoul , Republic of Korea b Department of Nuclear Medicine, Samsung Medical Center, Sungkyunkwan University School of Medicine, 50 Ilwon-Dong, Gangnam-Gu, Seoul , Republic of Korea article info Article history: Received 11 May 2010 Accepted 22 May 2010 Available online 4 June 2010 Keywords: Positron emission tomography Digital timing method Field-programmable gate array Geiger mode avalanche photodiode (GAPD) abstract A simple and improved digital timing method was developed for positron emission tomography (PET). This method, the so-called initial rise interpolation method, is based on an important characteristic of gamma signals: a properly pre-amplified and sampled gamma signal pulse can be characterized to arrive with an initial rise from the baseline and then reach a maximum rise. The pulse arrival time was obtained by calculating the intersection of the initial rise line with the baseline for each gamma signal pulse. Using an 8-channel 100 MHz free-running ADC and FPGA combined data acquisition (DAQ) card, three digital timing methods were employed to measure the coincidence timing resolution of two types of recently developed 3 mm 3 mm PET sensors (a fast and a slow GAPD). The results showed that the initial rise interpolation method provides the best timing resolution for both types of GAPDs: 0.7 ns FWHM for fast GAPD and 1.5 ns FWHM for slow GAPD (digital CFD: 1.5 and 2.2 ns FWHM; maximum rise interpolation: 1.8 and 2.7 ns FWHM). By implementing the initial rise interpolation method into the FPGA of DAQ card, PET images of two 18 F line sources were acquired successfully using a pair of 4 4 GAPD-LYSO array detectors (single pixel size: 3 mm 3 mm). The acquired image spatial resolution was a 3.1 mm FWHM. Furthermore, the simulation was performed to evaluate the effects of the pulse rise time, pulse amplitude and front end noise level on the timing resolution estimated using the three digital timing methods. In accordance with the measurement results, the simulation results also showed that the initial rise interpolation method provided the best timing resolution. These results show that this simple and improved digital timing method is reliable and useful for the development of high performance PET. & 2010 Elsevier B.V. All rights reserved. 1. Introduction The detection of annihilation gamma rays is the basic principle of positron emission tomography (PET). To improve the system flexibility and reduce analogue electronics, field-programmable gate arrays (FPGAs) are being used increasingly for gamma ray detection [1 5]. Moreover, a range of FPGA-based digital timing methods have been developed to measure the pulse arrival time instead of the analogue coincidence discrimination [6 10]. Digital constant fraction discrimination (DCFD) is the digital version of analogue constant fraction discrimination, which can provide better timing resolution than the other digital timing methods [7]. In this method, the digitized gamma signal pulse is delayed, amplified, inverted and then added to the original pulse. Thus, a unipolar pulse is transformed into a bipolar pulse. The pulse arrival time was calculated by linear interpolation between the n Corresponding author. Tel.: ; fax: addresses: ychoi.image@gmail.com, ychoi@skku.edu (Y. Choi). two zero-crossing samples [8]. In the DCFD method, the accuracy of the time mark is affected by the signal to noise ratio (SNR) and shape of the gamma signal pulse. The maximum rise interpolation (MRI) method detects the pulse arrival time by calculating the intersection of the maximum rise line with the baseline [6]. This method is simple and fast but the accuracy of the time mark is affected by the ADC sampling phase because the slope of the maximum rise line varies with the sampling phase of the ADC clock. The accuracy of this method can be improved using statistical methods but this method requires the post-processing of a large volume of data and the timing resolution for the coincidence channels with no delay even became worse [11]. Currently, a Geiger mode avalanche photodiode (GAPD)-based PET system is being developed in our laboratory. Good timing resolution is needed to reduce the ratio of random coincidences and achieve time-of-flight (TOF) PET imaging. The aim of this study was to develop a simple and improved digital timing method that can detect the pulse arrival time more accurately than commonly used digital timing methods. The initial rise interpolation (IRI) method was developed to detect pulse arrival /$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi: /j.nima

2 220 W. Hu et al. / Nuclear Instruments and Methods in Physics Research A 622 (2010) time based on the initial rise points of digitized gamma signal pulse. Three digital timing methods (IRI, DCFD and MRI) were implemented using an 8-channel 100 MHz free-running ADC and FPGA combined data acquisition (DAQ) card to measure the coincidence timing resolution of two types of recently developed GAPDs for PET. To prove the feasibility of high performance PET imaging using the IRI method, the PET images of two 18 F line sources were acquired using a pair of 4 4 (single pixel size: 3mm 3 mm) GAPD sensors combined with Cerium-doped Lutetium Yttrium Orthosilicate (LYSO) array crystals (single pixel size: 3 mm 3 mm 20 mm). Finally, a simulation was performed to evaluate the effects of the pulse rise time, pulse amplitude and front end noise level on the timing resolution estimated using the three digital timing methods. pulse with a positive and a negative peak. The timing point corresponding to the second point V(a+1) of the maximum rise line can be detected by peak sensing. Finally, 10 and 20 ns delayed pulses using this timing point can save the two points, V(a) and V(a 1), of the initial rise line. As shown in Fig. 4, after determining the initial rise line for each pulse, V(a 1) and V(a) were saved for an accurate arrival time calculation. The mean value of the 8 samples before the initial rise was calculated and used as the individual baseline for 2. Materials and methods 2.1. Pulse arrival time detection using initial rise interpolation method The initial rise interpolation (IRI) method is based on an important characteristic of the gamma signal: a properly preamplified and sampled gamma signal pulse can be characterized to arrive with an initial rise from the baseline and then increase to a maximum. Fig. 1 shows a typical pre-amplified gamma signal pulse digitized using a 100 MHz free-running ADC. The accurate pulse arrival time can be estimated by calculating the intersection of the initial rise line with the baseline for each pulse. It is quite similar to the maximum rise interpolation (MRI) method used in the ClearPET system [6,11,12]. However, attention should be paid to the different interpolation lines for these two methods, as shown in Fig. 2: the slope of initial rise line is less affected by the ADC sampling phase than the maximum rise line. For MRI method Fig. 2. Comparison of the MRI method and the IRI method. T MRI ¼ a Dt 1 ¼ a ðvðaþ baselineþ=ðvðaþ1þ VðaÞÞ ð1þ For IRI method T IRI ¼ a 1 Dt 2 ¼ a 1 ðvða 1Þ baselineþ=ðvðaþ Vða 1ÞÞ ð2þ Fig. 3 shows the initial rise finding algorithm. A 10 ns delayed pulse was subtracted from the original pulse to provide a bipolar Fig. 3. Initial rise finding algorithm: (1) Bipolar pulse generation, (2) positive peak detection and (3) trigger generation for initial rise line. Fig. 1. Typical pre-amplified gamma signal pulse digitized by a 100 MHz free-running ADC. Fig. 4. Signal processing steps to detect the pulse arrival time based on the IRI method.

3 W. Hu et al. / Nuclear Instruments and Methods in Physics Research A 622 (2010) each pulse, which is used for the accurate time calculation and energy calibration. The pulse energy was acquired by multiplying by 1/32 and the integration value of 32 samples, and the baseline value was subtracted. The time mark T a 1 was saved as the coarse arrival time. After all signal processing steps were complete, the accurate pulse arrival time, T IRI, was finally calculated using the following equation: T IRI ¼ a 1 Dt 2 ¼ a 1 ðvða 1Þ baselineþ=ðvðaþ Vða 1ÞÞ ¼ a 1 ðvða 1Þ ðvða 2ÞþVða 3Þ þþvða 9ÞÞ=8Þ=ðVðaÞ Vða 1ÞÞ ð3þ and shaped to have an approximately 320 ns pulse width and a 500 mv peak value. The pre-amplified signals were then acquired using the DAQ card implemented with 3 different digital timing methods (IRI, DCFD and MRI). The timing resolution was also compared using the two types of baselines (individual baseline and common baseline) for an accurate pulse arrival time calculation in the IRI method. Fig. 6 shows the experiment setup for the coincidence timing resolution measurement Hardware implementation In this study, a VHS-ADC Virtex-4 card (Lytech Inc., Canada) was used for data acquisition and processing. VHS-ADC Virtex-4 is a FPGA-based DAQ card, which has an 8-channel 14-bit 100 MHz free-running ADC, a Xilinx Virtex-4 FPGA and a 128 MB SDRAM. The FPGA programming was facilitated using a model-based design on Matlab Simulink (Mathworks, USA), Xilinx system generator (Xilinx, USA) and VHS-ADC libraries (Lyrtech Inc., Canada). No hardware language (VHDL or Verilog) for FPGA pin mapping was needed because the Xilinx system generator can automatically convert the model-based FPGA code into a hardware recognizable bit file with the optimized hardware resource distribution. Data acquisition was controlled by the VHS control utility. Fig. 5 shows the VHS-ADC-based PET DAQ system Evaluation for digital timing methods and PET image acquisition Coincidence timing resolution measurement for PET sensors Considering the characteristics of the different PET sensors, which have different rising times, the coincidence timing resolution for two types of recently developed 3 mm 3 mm PET sensors was measured: a fast GAPD from Photonique (Geneva, Switzerland) and a slow GAPD from SensL (Cork, Ireland). A 10 mci 22 Na point source was placed in the center of the paired GAPDs coupled with LYSO crystals. Fast GAPD and slow GAPD were tested in turn. The coincidence gamma signals were pre-amplified Fig. 6. Experimental setup for the coincidence timing resolution measurements: 22 Na point source was placed in the center of the paired GAPDs coupled with LYSO crystals, and two channel ADCs were used for data acquisition. Fig. 5. VHS-ADC-based PET DAQ system: FPGA code was downloaded to the VHS-ADC card through VHS control utility and the host computer was used to control data acquisition and recording.

4 222 W. Hu et al. / Nuclear Instruments and Methods in Physics Research A 622 (2010) PET image acquisition for two 18 F line sources To demonstrate the feasibility of high performance PET imaging using this improved digital timing method, PET images of two 18 F line sources (0.4 mm inner diameter) were acquired by rotating the motor placed in the center of the paired 4 4 (single pixel size: 3 mm 3 mm) GAPD-LYSO array detectors for 1801 (61 by 30 times). The GAPD arrays were purchased from SensL (Cork, Ireland) and the LYSO array was obtained from Sinocera (Shanghai, China). Only 8-channel gamma signals (4 channels from GAPD array 1 and 4 channels from GAPD array 2) were acquired simultaneously because the VHS-ADC Virtex-4 card only has 8 channel ADCs. The pulse arrival time, energy and position of each gamma signal were saved on the host computer for coincidence sorting and image reconstruction. Fig. 7 shows the experimental setup for PET image acquisition for the two 18 F line sources Simulation for comparison of different digital timing methods A simulation study was carried out to determine the effects of the pulse rise time, pulse amplitude and front end noise level on timing resolution estimated using the three digital timing methods (IRI, DCFD and MRI). The ideal (noise free) gamma ray response pulse detected by PMT or GAPD combined with LYSO was modeled using a modified version of the single-photon PMT response function [13] hðtþ¼ta expð t=t rise Þ=t 2 rise : where h(t) denotes the gamma ray response pulse as a function of time t, t rise is the pulse rise time and A the amplitude-related constant of the gamma signal pulse. The coincidence timing resolution was affected mainly by three parameters: amplitude of the gamma signal pulse, pulse rise time and front end noise level. The ADC has a sampling rate of 100 MHz, 14-bit resolution and an input range of 1.25 to V. The pulse amplitude can be changed from 0.2 to 1.0 V by controlling the gain of the pre-amplifier board. The rise time of the output gamma signal from the GAPD-LYSO detector was changed from 20 to 60 ns by changing the resistance and capacitance of the pre-amplifier board. The acquired front end noise level (VHS-ADC) ranged from 10/ to 50/ V. Therefore, three different gamma pulses were simulated to examine the accuracy of the timing methods: ð4þ (1) At a low noise level (10/ V) and fast rise time (20 ns), change the amplitude of the gamma signal pulse (0.2, 0.4, 0.6, 0.8, 1.0 V). (2) At a high amplitude of the gamma signal pulse (1.0 V) and low noise level (10/ V), change the rise time (20, 30, 40, 50, 60 ns). (3) At a high amplitude (1.0 V) and fast rise time (20 ns), change the noise level (10/ , 20/ , 30/ , 40/ , 50/ V). 3. Results and discussion Fig. 7. Experimental setup for PET image acquisition: two 18 F line sources with different activities were placed on the motor between the two GAPD-LYSO arrays, 8-channel pre-amplified gamma signals were acquired using the VHS-ADC Virtex- 4 card. Table 1 Timing resolution by hardware implementation of the three different digital timing methods. Timing methods Fast GAPD (ns) Slow GAPD (ns) IRI DCFD MRI Coincidence timing resolution measurement for PET sensors Table 1 lists the timing resolution of the fast GAPD and slow GAPD estimated by hardware implementation of the 3 different digital timing methods (30% energy window). For fast GAPD, the timing resolution of the IRI method was 53% and 61% better than that of the DCFD and MRI methods, respectively. For a slow GAPD, the timing resolution of initial rise interpolation was 32% and 44% better than the DCFD and MRI methods, respectively. Fig. 8 presents the timing spectra for the three different digital timing methods. For the IRI method, Table 2 lists the timing resolution of the different types of baselines. Fig. 8. Timing spectra acquired using three different digital timing methods (30% energy window).

5 W. Hu et al. / Nuclear Instruments and Methods in Physics Research A 622 (2010) As the MRI method was affected more by the ADC sampling phase, the accuracy of the pulse arrival time was worse than that of the IRI method. The DCFD method provides better timing resolution than the maximum rise interpolation, but the accuracy of this method is limited by the number of points on the rising edge of the gamma signal pulse indicating that the timing resolution still requires improvement [10]. For hardware implementation, the IRI method was as simple as the maximum interpolation method. The experimental results show that it Table 2 Timing resolution (FWHM) estimated by the IRI using the different baselines. Fast GAPD (ns) Individual baseline Common baseline Slow GAPD (ns) provided the best timing resolution among the three digital timing methods. Furthermore, in this method, using the individual baseline for each pulse provided slightly better timing resolution than using the common baseline. However, to achieve better performance using this digital timing method, the gamma ray pulse should be pre-amplified to an optimized pulse width and peak value. In addition, the resolution and sampling rate of the free-running ADC will affect the timing resolution PET image acquisition for two 18 F line sources PET images of the two 18 F line sources were acquired and reconstructed using the ordered subset expectation maximization (OSEM) reconstruction method. The two 18 F line sources can be distinguished easily, as shown in Fig. 9, and the acquired image spatial resolution was 3.1 mm FWHM. These results suggest that Fig. 9. PET image of two 18 F line sources (0.4 mm inner diameter): the line source placed on the right side has more activity, as shown on the reconstructed image (left), and the profile shows a spatial resolution of 3.1 mm FWHM (right). Fig. 10. Timing resolution as a function of the pulse amplitude (a), pulse rise time (b) and noise level (c).

6 224 W. Hu et al. / Nuclear Instruments and Methods in Physics Research A 622 (2010) the improved simple digital timing method can be used for high performance PET imaging Simulation for comparison of different digital timing methods Fig. 10 shows the timing resolution as functions of pulse amplitude, pulse rise time and noise level for the three different digital timing methods (IRI, MRI and DCFD). For all digital timing methods, the timing resolution improved with increase in pulse amplitude, as the pulse rise time and noise level decreased. Under all conditions, the IRI method always provides better timing resolution than the other two methods. Based on these simulation results, the IRI method provides the best timing resolution under the various gamma pulse conditions, which is in accordance with the hardware experimental results. 4. Conclusions The initial rise interpolation method was developed to accurately detect the pulse arrival time by calculating the intersection of the initial rise line with the baseline for each pulse. This method is simple and can provide better timing resolution than the digital CFD and maximum interpolation methods for various gamma pulses encountered in PET applications, which was demonstrated by both hardware measurements and simulation results. Good spatial resolution PET images of the two 18 F line sources were acquired, which demonstrated the feasibility of high performance PET imaging using this digital timing method. Based on the acquired experimental results, it was concluded that this simple and improved digital timing method is reliable and feasible for high performance PET systems. Acknowledgments This study was supported by a grant of the Converging Research Center Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( ), and by a grant of the Technology Innovation Program funded by, the Ministry of Knowledge Economy ( ), Republic of Korea. References [1] M. Streun, G. Brandenburg, H. Larue, E. Zimmermann, K. Ziemons, H. Halling, Nucl. Instr. and Meth. A 486 (2002) 18. [2] C.M. Laymon, R.S. Miyaoka, B.K. Park, T.K. Lewellen, IEEE Trans. Nucl. Sci. NS-50 (5) (2003) [3] M.S. Judenhofer, B.J. Pichler, S.R. Cherry, Phys. Med. Biol. 50 (2005) 29. [4] A. Mann, B. Grube, I. Konorov, S. Paul, L. Schmitt, D.P. McElroy, et al., IEEE Trans. Nucl. Sci. NS-53 (1) (2006) 297. [5] P. Guerra, J. Espinosa, J.E. Ortuno, G. Kontaxakis, J.J. Vaquero, M. Desco, et al., IEEE Trans. Nucl. Sci. NS-53 (1) (2006) 770. [6] M. Streun, G. Brandenburg, H. Larue, E. Zimmermann, K. Ziemons, H. Halling, Nucl. Instr. and Meth. A 487 (2002) 530. [7] M.A. Nelson, B.D. Rooney, D.R. Dinwiddie, G.S. Brunson, Nucl. Instr. and Meth. A 505 (2003) 324. [8] R. Fontaine, M.A. Tetrault, F. Belanger, N. Viscogliosi, R. Himmich, J.B. Michaud, et al., IEEE Trans. Nucl. Sci. NS-53 (3) (2006) 784. [9] A. Fallu-Labruyere, H. Tan, W. Hennig, W.K. Warburton, Nucl. Instr. and Meth. A 579 (2007) 247. [10] P. Guerra, J.E. Ortuño, G. Kontaxakis, M.J. Ledesma-Carbayo, J.J. Vaquero, M. Desco, et al., IEEE Trans. Nucl. Sci. NS-55 (5) (2008) [11] M. Streun, G. Brandenburg, M. Khodaverdi, H. Larue, C. Parl, K. Ziemons, NSS-MIC Conf. Rec. 4 (2005) [12] K. Ziemons, E. Auffray, R. Barbier, G. Brandenburg, P. Bruyndonckx, Y. Choi, et al., Nucl. Instr. and Meth. A 537 (2005) 307. [13] P. Guerra, J.E. Ortuño, J.J. Vaquero, G. Kontaxakis, M. Desco, A. Santos, IEEE Trans. Nucl. Sci. NS-53 (3) (2006) 1150.