Performance Characterization of the SAFIR Prototype PET Insert

Background: The SAFIR prototype insert is a preclinical Positron Emission Tomography (PET) scanner built to acquire dynamic images simultaneously with a 7 T Bruker Magnetic Resonance Imaging (MRI) scanner. The insert is designed to perform with an excellent coincidence resolving time of 194 ps Full Width Half Maximum (FWHM) and an energy resolution of 13 . 8% FWHM. These properties enable it to acquire precise quantitative images at activities as high as 500 MBq suitable for studying fast biological processes within short time frames ( < 5 s). In this study, the performance of the SAFIR prototype insert is evaluated according to the NEMA NU 4-2008 standard while the insert is inside the MRI without acquiring MRI data. Results: Applying an energy window of 391 − 601 keV and a coincidence time window of 500 ps the following results are achieved. The average spatial resolution at 5 mm radial oﬀset is 2 . 6 mm FWHM when using the Filtered Backprojection 3D Reprojection (FBP3DRP) reconstruction method, improving to 2 . 3 mm when using the Maximum Likelihood Expectation Maximization (MLEM) method. The peak sensitivity at the center of the scanner is 1 . 06% . The Noise Equivalent Count Rate (NECR) is 799 kcps at the highest measured activity of 537 MBq for the mouse phantom and 121 kcps at the highest measured activity of 624 MBq for the rat phantom. The NECR peak is not yet reached for any of the measurements. The scatter fractions are 10 . 9% and 17 . 8% for the mouse and rat phantoms, respectively. The uniform region of the image quality phantom has a 3 . 0% STD, with a 4 . 6% deviation from the expected number of counts per voxel. The spill-over ratios for the water and air chambers are 0 . 18 and 0 . 17 , respectively. Conclusions: The results satisfy all the requirements initially considered for the insert, proving that the SAFIR prototype insert can obtain dynamic images of small rodents at high activities ( ∼ 500 MBq) with a high sensitivity and an excellent count-rate performance.


Background
SAFIR (Small Animal Fast Insert for mRi) is a preclinical Positron Emission Tomography (PET) insert designed for a 7 T Bruker BioSpin 70/30 Magnetic Resonance Imaging (MRI) scanner [1,2]. It has been designed following the need to measure fast biological processes such as cerebral blood flow of small rodents [3]. The main requirements are precise quantitative PET images of [ 15 O]H 2 O with a spatial reso-lution of ∼2 mm, a temporal resolution of < 5 s and a quantitative voxel accuracy better than 10%. This implies measurements with activities as high as ∼500 MBq for sufficient counting statistics. High rate capability in turn requires short coincidence resolving time (<500 ps) and small coincidence time window (∼500 ps) in order to reduce the number of random coincidences [2,4].
Since these requirements cannot be fulfilled by any other preclinical PET scanners [5][6][7][8][9][10][11][12][13][14][15][16], we have designed the Small Animal Fast Insert for mRi (SAFIR) system. The prototype version of SAFIR has been built and initially characterized, showing an excellent time resolution of 194 ps and an energy resolution of 13.8% [17][18][19]. In this study, we evaluate the SAFIR prototype performance according to the National Electrical Manufacturers Association NU 4-2008 standard [20] which we refer to as NEMA in the rest of this paper. In addition, the energy resolution and the Coincidence Resolving Time (CRT) of the scanner are studied as a function of activity.

The SAFIR Prototype PET Insert
The SAFIR prototype PET insert comprises 2880 lutetium-yttrium oxyorthosilicate (LYSO) crystals arranged into 16 rings with a crystal-to-crystal distance of 128.1 mm. It covers an axial field of view of 35.6 mm. The insert is designed as a dodekagon with 12 identical sectors. Each sector hosts two detector modules. Each detector module comprises two LYSO crystal matrices, one made of 8 × 7 and one made of 8 × 8 crystals with 2.12 × 2.12 × 13.0 mm 3 size arranged on a grid with 2.2 mm pitch, using enhanced specular reflector foil (3M Vikuiti Enhanced Reflector Films) as spacer. Hence, the detector head in each sector is made of 2 × 2 parallel crystal matrices with 0.6 mm gap, aligning 16 crystals in axial direction times 15 crystals in transaxial direction. The crystal matrices are one-to-one coupled to Silicon Photo-Multiplier (SiPM) arrays (Hamamatsu S13361-2050 AE-08 SPL MPPC) with 2.2 mm pitch. Two crystal matrix and SiPM array assemblies are in turn mounted onto one detector module board hosting at the same time four PETA6SE Application-Specific Integrated Circuits (ASICs) [21].

Data Acquisition and Data Processing
The PETA6SE ASICs provide digitised energy and timing information of hits in the crystals, which are continuously read out by means of Field Programmable Gate Arrays (FPGAs) and transferred to the Data Acquisition (DAQ) computer via 12 optical Ethernet links (1 Gbit/s each).
The data are acquired with identical settings for the overvoltage of the SiPM arrays (6 V), the readout frequency (280 MHz) and the energy threshold (30 LSB, corresponding to 100 keV) of the PETA6SE ASIC. For all measurements, we applied a relative timing threshold of 75 LSB (corresponding to 45 mV), except for the scatter fraction and count rate measurements, where timing thresholds of 150 LSB (corresponding to 90 mV) and 250 LSB (corresponding to 150 mV) were used. This is required for the proper functioning of the SAFIR prototype at high activities up to 500 MBq.
The acquired raw data are processed off-line. We apply energy and timing calibrations converting time counter information into time stamps in picosecond and Charge to Digital Converter (QDC) values into energies in electron volt [19]. These calibrated hit data are filtered by an energy window of 391−601 keV and sorted into coincidence events using the single window method and a coincidence time window of 500 ps. Coincidence events with more than two singles as well as those with a tangential angle between the singles smaller than 90 • are eliminated. The resulting coincidence data set is stored in list mode. The same processing parameters are applied to all data reported below. For the peak sensitivity measurement, we create a second coincidence data set, by filtering and sorting the data using a larger energy window of 250 − 650 keV in addition to the one mentioned above.
We use Software for Tomographic Image Reconstruction (STIR) for the image reconstruction [22]. The coincidence data sets, stored in list mode, are sorted into three-dimensional (3D) projection data, which are then reconstructed into images. We employ two reconstruction methods: 1) Filtered Backprojection 3D Reprojection (FBP3DRP) [23] and 2) Maximum Likelihood Expectation Maximization (MLEM) [24]. The voxel size is 0.55 × 0.55 × 1.1 mm 3 . When we perform MLEM reconstructions, we use 30 iterations and apply a Gaussian filter with a Full Width Half Maximum (FWHM) of 1.1 × 1.1 × 2.2 mm 3 after each iteration, except for the reconstruction of the spatial resolution data, where NEMA requires a reconstruction without any filtering.
In the FBP3DRP method, a cylindrical scanner model with an equidistant spacing of crystals in axial and transaxial direction is used while in the MLEM method, the scanner is modeled with the exact generic geometry [25]. It has been shown that using a more accurate model of the scanner improves the image quality [26].

Characterization of the SAFIR prototype insert
The performance of the SAFIR prototype insert is characterized according to the NEMA protocol while it is inside the MRI scanner without acquiring MRI data. In addition, the energy resolution and the CRT of the insert are evaluated at different activities up to 537 MBq using the NEMA mouse scatter phantom.

Spatial resolution
We measure the spatial resolution using a 22 Na point source (Eckert & Ziegler Isotope Products, MMS09-022), with an activity of 0.487 MBq and a source diameter of 0.25 mm centered in an acrylic cube of 10 mm edge length. We acquire data from the point source for two axial positions of 0.0 mm and 8.9 mm (equivalent to a quarter of the axial field of view (FOV)) and for 10 radial positions from 0.0 mm to 45.0 mm in steps of 5.0 mm. At least 10 5 coincidence events are collected per source position.
We reconstruct the images of the point source using a) FBP3DRP and b) MLEM without any smoothing. The FWHM and Full Width Tenth Maximum (FWTM) of the images are obtained according to NEMA.

Sensitivity
We measure the sensitivity using the the same point source as for the spatial resolution measurements (section 2.3.1). The source is located on the central axis of the scanner and is axially moved in steps of 1 mm starting from the axial offset of −15 mm and ending with the axial offset of 15 mm. We collect 8 × 10 4 coincidence events per source position. The sensitivity at each axial position is calculated according to NEMA. The system sensitivities for mouse and rat are not calculated as SAFIR has a shorter axial FOV than required by NEMA.

Count Rate Performance and Scatter Fraction
We use NEMA mouse and rat scatter phantoms to measure count rate performance and scatter fraction. We use an 18 F labeled radiotracer as the radioactive source. The start and end activities are 537 MBq and 0.22 MBq for the mouse phantom, and 624 MBq and 1 MBq for the rat phantom, respectively. At least 5 × 10 5 coincidence events are collected per acquisition. Data analysis is performed according to NEMA to obtain the total, true, scattered and random count rates as well as the Noise Equivalent Count Rate (NECR) and the system Scatter Fraction (SF).

Energy Resolution and Coincidence Resolving Time
Using the data set collected with the mouse scatter phantom for the count rate measurement (section 2.3.3), we evaluate as well energy resolution and CRT as a function of activity. We report FWHM of a Gaussian fit (480 − 580 keV) to the coincidence energy spectrum as the energy resolution. The maximum of the coincidence timing spectrum is obtained by a parabolic fit through the highest bin and its two neighbours. We measure the FWHM of the spectrum by linearly interpolating between the bins at half the maximum and report the width as coincidence timing resolution [19].

Image Quality Study
We use the NEMA image quality phantom comprising: 1) two cold chambers, one filled with water and one filled with air, 2) five hot rods of (1, 2, 3, 4 and 5) mm diameters and 3) a uniform region. We fill the phantom with an 18 F labeled radiotracer. According to NEMA, the measurement should be done with an initial activity of 3.7 MBq and an acquisition time of 20 min. Since the SAFIR prototype insert does not cover the whole length of the phantom, we run the measurement in two bed positions and modify activity and acquisition time such that the same number of annihilations are produced in both bed positions, taking into account the decay of the activity. In the first bed position, the cold rods together with the uniform region are measured with an initial activity of 4.2 MBq for 25 min and in the second bed position, the hot rods are measured with an initial activity of 3.3 MBq for 32 min.
We reconstruct the data using MLEM with random, attenuation, scatter and normalization corrections embedded into the reconstruction algorithm. In addition, we calibrate the reconstructed image providing absolute voxel values and thus quantitative PET data. Both, data corrections and the quantitative calibration are described below.
In addition to the above mentioned values and to evaluate the accuracy of the image, we calculate the deviation of the absolute voxel value as follows: where m is the measured mean value of the uniform region and E is the expected voxel value.
We apply the following corrections to obtain quantitative PET data: • Random correction: We estimate the number of random coincidences per Line of Response (LOR) using the singles-prompt method introduced by J.F. Oliver et al. [27]. This method is an extension of the singles-rate method [28], outperforming the singles-rate method at high activities. • Attenuation correction: The attenuation maps of the phantoms and the bed are generated based on their known geometries, the material compositions and their corresponding attenuation coefficients taken from the National Institute of Standards and Technology (NIST) reference database [29]. The attenuation correction factors are calculated using these maps.
• Scatter correction: We use the Single Scatter Simulation (SSS) method implemented in STIR to estimate the number of scattered events that occurred in the phantom [30,31]. In this method, the attenuation map and the scanner geometry are down-sampled in order to accelerate the computation. We use a down-sampling factor of two.
• Detector normalization: We employ the direct normalization method to obtain the normalization factors [32,33]. A cylinder phantom of 74 mm diameter and 50 mm length uniformly filled with an 18 F labeled tracer is located in the center of the scanner. The data are acquired with a starting activity of 141 MBq for ∼14 h, resulting in a total number of 2.65 × 10 9 coincidences and an average number of 1768 counts per LOR. The normalization factors are obtained by correcting for different lengths of intersection between the LOR and the cylinder volume and the effects of attenuation, scatter and randoms in the collected data.   3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 3 Results and Discussion Table 1 and figure 1 show the spatial resolution results for the axial positions of 0.0 mm and 8.9 mm using FBP3DRP and MLEM. The MLEM algorithm yields better spatial resolution results than the FBP3DRP method. For instance, the average FWHM over radial, tangential and axial directions at the 5 mm radial offset and 0.0 mm axial offset is 2.6 mm for the FBP3DRP method and 2.3 mm for the MLEM method. Using FBP3DRP, the spatial resolution especially degrades with respect to FWTM due to the streak artifact that is present in the reconstructed image. The FWHM in radial direction degrades toward the edge of the scanner due to the parallax effect.

Spatial Resolution
We compare the SAFIR prototype results with a group of preclinical PET scanners, referred to as reference scanners in this paper [5][6][7][8][9][10][11][12][13][14][15]. Among these scanners, Hyperion II D and nanoScan are for combined PET-MRI systems and Bruker is designed for the same MRI system for which SAFIR is designed. Table 2 presents the spatial resolution of SAFIR and the reference scanners. PET scanners of similar crystal size yield a slightly better spatial resolution than the SAFIR prototype when using FBP3DRP reconstruction. This is related to the reconstruction algorithm in combination with the geometry of the scanner. For scanners of relatively large detector heads such as SAFIR with (8 + 7) × 8 crystals per module, the FBP3DRP method introduces error, as this method requires regularly spaced projection data which in turn requires regularly spaced detector elements. Interpolating the crystal positions into a regular space causes artifacts in the image and degrades the spatial resolution. The iterative algorithm does not require interpolation. It uses the exact generic geometry and thus yields better results. In addition, all scanners in table 2 with a similar crystal size as SAFIR have a shorter crystal length, except 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62   for LabPET 8 which uses depth of interaction information and has a continuous arrangement of the crystals on a ring. Figure 2 shows the total sensitivity calculated for the point source data measured at different axial positions. The maximum sensitivity at the center is 1.06 % for the energy window of 391 − 601 keV. It decreases to 0.2 % at 15 mm axial offset. The expected triangular profile is clearly visible. Table 3 compares the peak sensitivity of SAFIR and the reference scanners. The scanners have different axial FOVs and use different energy windows. Given its short axial FOV, the SAFIR prototype yields a high sensitivity which is in line with our goal for SAFIR.

Count Rate Performance and Scatter Fraction
Count rate results as a function of the activity in the phantom are plotted in figure 3, for the mouse and rat phantoms and for two relative timing thresholds of 90 mV and 150 mV. The NECR peak is not reached for any of the measurements. This proves that the SAFIR prototype insert is capable of handling activities higher than 500 MBq.

FWHM (mm) a System
Recon. method crystal size (mm 3    concentration of 2690 MBq/ml) for the mouse scatter phantom and 121 kcps at 624 MBq (corresponding to an activity concentration of 1390 MBq/ml) for the rat scatter phantom. Due to the relatively short FOV of the SAFIR prototype, the detector receives many single γ-rays for the rat scatter phantom from outside the FOV, resulting in many randoms.

Image Quality Analysis
• All images are artifact-free.
• The Spill-Over Ratio for the water/air chamber is 0.18/0.17 (table 7).
• The recovery coefficients for the smallest and largest rods are 0.13 and 0.88, respectively (table 8). • The smallest hot rod (1 mm diameter) is not visible in the image.
The deviation of the absolute voxel value in the uniform region is 4.6% ± 6.5%. For the uncertainty, we only propagated the uncertainties of the measurement of the activity and the volume of the image quality phantom.
The Spill-Over Ratios of the air and water chambers are almost identical (0.01 difference), which is a direct result of including the data corrections into the reconstruction. Especially, the attenuation and scatter corrections influence the amount of background noise in the cold chambers with different attenuation properties.  There is a strong correlation between the crystal size and the spatial resolution and thus with the recovery coefficient. SAFIR's performance in terms of recovery coefficient is comparable with the scanners of similar crystal size (table 9). However, scanners of smaller crystals such as [5,8] and the Bruker scanner [15] with monolithic LYSO crystals outperform SAFIR.

Conclusion
The performance of the SAFIR prototype insert has been evaluated according to the NEMA NU 4-2008 standard while the insert was inside the 7 T MRI scanner without acquiring MRI data. The MRI-compatibility of the insert has been tested in previous studies [19,36].
The results satisfy all requirements initially considered for the insert. The SAFIR prototype yields a high sensitivity for its short axial coverage. The count rate measurement results in an excellent NECR value of 799 kcps at the highest measured activity of 537 MBq using the mouse phantom, while not yet reaching the NECR peak. This demonstrates the prototype capability to handle high rate measurements, appropriate for dynamic imaging of fast biological processes. The spatial resolution has been shown to be as good as for other preclinical scanners with similar crystal size. The tests performed using the image quality phantom present a high uniformity and accuracy for the reconstructed images, suitable for quantitative PET imaging.
The final version of the SAFIR insert is being developed with the same components as of the prototype but a quadrupled axial coverage, allowing dynamic whole body imaging of a mouse in a single bed position. This will also results in a higher sensitivity and NECR, especially for the rat scatter phantom as the contribution of the out-of-FOV γ-rays to the random count rate decreases.