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Preliminary Resolution Performance of the Prototype System for a 4-Layer DOI-PET Scanner: jPET-D4 Taiga Yamaya, Naoki Hagiwara, Takashi Obi, Tomoaki Tsuda, Keishi Kitamura, Tomoyuki Hasegawa, Hideaki Haneishi, Naoko Inadama, Eiji Yoshida, and Hideo Murayama
Abstract—We are developing a high-performance brain PET scanner, jPET-D4, which provides 4-layer depth-of-interaction (DOI) information. The scanner is designed to achieve not only high spatial resolution but also high scanner sensitivity with the DOI information obtained from multi-layered thin crystals. The scanner has 5 rings of 24 detector blocks each, and each block consists of 1024 GSO crystals of 2.9 mm 2.9 mm 7.5 mm, which are arranged in 4 layers of 16 16 arrays. At this stage, a pair of detector blocks and a coincidence circuit have been assembled into an experimental prototype gantry. In this paper, as a preliminary experiment, we investigated the performance of the jPET-D4’s spatial resolution using the prototype system. First, spatial resolution was measured from a filtered backprojection reconstructed image. To avoid systematic error and reduce computational cost in image reconstruction, we applied the DOI compression (DOIC) method followed by maximum likelihood expectation maximization that we had previously proposed. Trade-off characteristics between background noise and resolution were investigated because improved spatial resolution is possible only when enhanced noise is avoided. Experimental results showed that the jPET-D4 achieves better than 3mm spatial resolution over the field-of-view. Index Terms—Depth-of-interaction (DOI), maximum likelihood expectation maximization (ML-EM), positron emission tomography (PET), statistical image reconstruction.
I. INTRODUCTION OSITRON emission tomography (PET) has become one of the most important imaging technologies in neurosciences, and PET scanners are desired that can visualize fine neuronal functions for better understanding of pathophysiological brain conditions. To fulfill this desire, we are developing a high-performance brain PET scanner, jPET-D4, which provides depth-of-interaction (DOI) information. This scanner is designed to achieve not only high spatial resolution but also high scanner sensitivity with the DOI information [1] obtained from multi-layered thin crystals. Fig. 1 shows the latest design
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Manuscript received November 15, 2004; revised January 31, 2006. T. Yamaya, N. Inadama, E. Yoshida, and H. Murayama are with the National Institute of Radiological Sciences, 4-9-1 Anagawa, Inage-ku, Chiba 2638555, Japan (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). N. Hagiwara and T. Obi are with the Tokyo Institute of Technology, Yokohama, Japan (e-mail:
[email protected];
[email protected]). T. Tsuda and H. Haneishi are with Chiba University, Chiba, Japan (e-mail:
[email protected];
[email protected]). K. Kitamura is with the Shimadzu Corporation, Kyoto, Japan (e-mail:
[email protected]). T. Hasegawa is with Kitasato University, Sagamihara, Japan (e-mail:
[email protected]). Digital Object Identifier 10.1109/TNS.2006.871901
Fig. 1. Geometric design of the jPET-D4.
of the jPET-D4 scanner. The scanner has 5 rings of 24 detector blocks each, and each block consists of 1,024 GSO crystals of 2.9 mm 2.9 mm 7.5 mm, which are arranged in 4 layers of 16 16 arrays. The detector rings have a diameter of 390 mm. At this stage, a pair of detector blocks and a coincidence circuit have been assembled into an experimental prototype gantry. In this paper, as a preliminary experiment, we investigate the performance of the jPET-D4’s spatial resolution using the prototype system. II. MATERIALS AND METHODS A. The Prototype System The prototype system consists of a pair of DOI detector blocks and a coincidence circuit. The prototype gantry has the same dimensions as that of the jPET-D4. The placement position of block detectors is manually adjustable so that all the required data can be measured. Fig. 2 shows the experimental setup. A block detector consists of a 4-layered 16 16 array of GSO crystals (Hitachi Chemical Co., Japan) with different amounts of cerium (Ce) dopant (0.5 mol%Ce for 1st and 2nd layers, and 1.5 mol%Ce for 3rd and 4th layers) and a 256 channel flat-panel position-sensitive photomultiplier tube (H9500: Hamamatsu Photonics K.K., Japan). The basis for DOI discrimination is the inserted reflector [1] that controls the distribution of scintillation light so that each position can be identified by the Anger type calculation. Four-layer DOI positions are identified based
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Fig. 3. DOI order charts for the jPET-D4. Four DOI layers result in 16 pairs of DOI layers. The order of pairs was numbered starting from the front pairs to the rear pairs of a DOI layer (a). For comparison, 2-layer case (b) and non-DOI case (c) were also implemented by the simple sum of the DOI data.
Fig. 2. Experimental setup of the prototype system for the line source measurement.
on this idea after upper and lower two DOI positions are separated by pulse shape discrimination [2]. Coincidence events that are detected within the energy window of 400 keV–600 keV are stored in a list-mode data format. B. Experiments Spatial resolution of three positions, at the center, and 50 mm and 100 mm off-center, were measured using a Ge- Ga line source (Fig. 2). The line source was covered with stainless steel (55 mm length, 1 mm internal diameter and 1.6 mm external diameter). In order to minimize the effects of dead-time, random events and scattering, the line source was surrounded by a lead cylinder (20 mm internal diameter and 120 mm external diameter) which had a 2 mm slit on the horizontal diameter. Thus measurements were restricted to the 2-D mode single slice scan, and the count rate was less than 100 cps. Twelve positions were measured at the center and 28 positions each were measured for the two off-center positions. After extracting the direct slice data, 284 279 counts were obtained. C. FBP Image Reconstruction The filtered backprojection (FBP) was applied to evaluate spatial resolution of the jPET-D4. First the list mode data were transformed into a sinogram. In order to avoid sampling errors due to the irregular sampling of DOI detectors, a new histogram method [3] was applied. In this method, two crystal positions in each event, which determine a line-of-response (LOR), were determined statistically according to the detection probability. The detection probability was calculated based on detector response functions (DRFs). Next the FBP with a ramp filter without cutoff was applied. A field-of-view (FOV) was 256 mm in diameter, and the sinogram was sampled in 256 detectors and 256 views. We have not done any correction including normalization yet. D. ML-EM Image Reconstruction Algebraic or statistical image reconstruction methods, such as the algebraic reconstruction technique (ART) [4] and the maximum likelihood expectation maximization (ML-EM) [5], have
been successfully used to improve image quality through accurate system modeling, though they are computationally burdensome. In order to reduce computational cost while maintaining the image quality, we previously proposed a DOI compression (DOIC) method [6]. In this work, we also applied the DOIC method followed by the ML-EM with accurate system modeling. 1) System Modeling: First the list mode data were transformed into a histogram without any interpolation. We restricted image reconstruction to histogram-based 2-D implementation, though our final goal is the full 3-D list-mode image reconstruction. Elements of the system matrix were defined as inner products of DRFs and image basis functions. The DRFs were computed by ray-tracing of gamma-rays in consideration of the geometrical arrangement and the penetration of crystals. The blurring effect caused by Compton scattering was not included in the DRFs. The image basis functions were a pixel of 1 mm in width. The FOV was restricted to 250 mm in diameter. Details of the system modeling are described in [6]. An on-the-fly system matrix calculation is commonly implemented in 3-D image reconstruction. In this paper, however, we pre-computed the system matrix and stored it because the size of the 2-D system matrix is within the limits of practical implementation. 2) DOI Compression: Four DOI layers result in 16 pairs of DOI layers. The order of DOI-layer pairs was numbered starting from the front pairs to the rear pairs of a DOI layer [Fig. 3(a)]. The DOIC method is based on redundant characteristics of the DOI-PET imaging system, such as high correlation of the DRFs and low sensitivity of deep DOI layers. Detector crystals in rear DOI layers, which detect only gamma-rays penetrating the surface crystals, have lower sensitivity than those of front DOI layers. In the case of the jPET-D4, for example, the sensitivity of the 16th pairs of DOI layers (i.e., a detector crystal pair in the 4th DOI layer) is about 5% of that of the 1st pairs of DOI layers. In addition to the low sensitivity of deep DOI layers, the neighboring DRFs of different DOI-layer pairs correlate with each other. The DOIC method combines deep pairs of DOI layers to 16) into shallow pairs of DOI layers (from 1 (from to ) whose DRFs highly correlate. The correlation of DRFs is simply calculated as closeness of LORs in order to avoid a computational burden. Our previous study [6] showed was the optimum value for the jPET-D4. Thus the number of the data elements is reduced while all detected events are preserved.
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Fig. 4. An illustration of the combined phantom. Simulated uniform backgrounds of 40 mm diameter were added to the measured line source data. The dotted circles are the ROIs for background noise evaluation.
Resolution loss for compressed DOI-PET data can also be minimized because data bins of front DOI-layer pairs, which highly contribute to the imaging, are preserved. We note that the DOIC method preserves the Poisson distribution since the transformation is a simple summation. 3) Image Reconstruction: In order to avoid over-estimation for point source objects, uniform backgrounds were added to the line sources. In this paper, we used Monte Carlo simulated data as the background, because obtaining high-count data takes a great deal of time for the prototype system. We simulated three uniform cylinders of 40 mm diameter which were placed at the center and 50 mm and 100 mm off-center (Fig. 4). Total counts of the three uniform cylinders were about 10 M. A ring phantom of 280 mm diameter was also simulated for normalization. In order to improve accuracy of normalization factors, normalization data were averaged considering block detector symmetry. Details of the Monte Carlo simulator are described in [7]. In this paper, we applied the DOIC followed by normalization-weighted ML-EM [8] (DOIC-ML-EM). DRFs were normalized instead of measurement data in order to preserve the Poisson distribution of the data. As a preliminary experiment, actual DRFs of the prototype system were assumed to be equal to those of the Monte Carlo simulation because normalization scan takes a great deal of time for the prototype system. This assumption was acceptable because the unmatched normalization affects the uniform backgrounds rather than the point source objects. Therefore the normalization factors were obtained by comparing Monte Carlo simulated data and analytical data of the ring phantom. The analytical data were calculated based on the modeled DRFs. E. Resolution Evaluation 1) 4-Layer DOI vs. 2-Layer DOI and Non-DOI: In order to evaluate the 4-layer DOI effect, we also implemented 2-layer and non-DOI cases by simple summing of the DOI data. In the 2-layer and the non-DOI cases, 16 pairs of DOI layer were grouped into 4 pairs and 1 pair, respectively [Fig. 3(b), (c)].
Fig. 5. Reconstructed images using the FBP with (a) 4-layer DOI, (b) 2-layer DOI, and (c) non-DOI. 100 160 pixels were extracted and displayed from 256 256 pixels images.
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Fig. 6. Radial and tangential FWHMs of the FBP reconstruction with 4-layer DOI, 2-layer DOI and non-DOI.
2) Figures of Merit: Two figures of merit, background noise and spatial resolution were used to evaluate the image quality. The background noise was measured as the normalized standard deviation (NSD), defined as (1) where and are the variance and the mean value of counts in regions of interest (ROIs), respectively. The ROIs are shown in Fig. 4. Local NSD values were measured for the center, 50 mm off-center and 100 mm offcenter using 4 ROIs each around the line source. An averaged NSD was also measured using 12 ROIs. The spatial resolution was measured as the average of radial and tangential full widths at half maximum (FWHMs) after subtracting the background. It should be noted that blurring by the source diameter of 1.6 mm was not deconvoluted. A local
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Fig. 7. Graphs showing the trade-off between the background noise (NSD) and the FWHM. Local trade-off graphs at the center (a), 50 mm off-center (b) and 100 mm off-center (c) are plotted. The trade-off between the averaged NSD and the averaged FWHM is shown in (d). (a) Center, (b) 50 mm off-center, (c) 100 mm off-center, (d) Average.
FWHM was defined for each position, and an averaged FWHM was defined as the average of three local FWHMs.
III. RESULTS AND DISCUSSIONS
A. FBP Image Reconstruction The line source data with 4-layer DOI, 2-layer DOI and non-DOI were reconstructed using the FBP. Reconstructed images and plots of FWHM are shown in Figs. 5 and 6, respectively. In Fig. 5, we see that point spread functions (PSFs) become circular in the 4-layer DOI case, while they are noncircular in the peripheral regions in 2-layer and non-DOI cases. Streak artifacts appear because normalization including detector-block gap correction was not applied at this development stage. Fig. 6 shows that 1) radial FWHMs at the center are almost the same (3.17 mm with 4-layer DOI, 3.20 mm with 2-layer DOI, and 3.31 mm with non-DOI), 2) a radial FWHM at 100 mm off-center of the 4-layer DOI case is improved to 4.23 mm while those of the 2-layer DOI and non-DOI cases are 5.51 mm and 9.51 mm, respectively. Resolution uniformity is much improved by using 4-layer DOI information. Spatial resolutions of the jPET-D4 are estimated as 3.0 mm (center) and 4.1 mm (100 mm off-center). Taking into account the diameter of the line source, the spatial resolution was roughly , where we assumed that PSFs calculated as were a Gaussian and we modeled the line source including a positron range effect as a Gaussian of 1.0 mm FWHM (i.e., the inner diameter of the line source).
B. ML-EM Image Reconstruction Trade-off characteristics between background noise and resolution are also important because improved spatial resolution is possible only when enhanced noise is avoided. The trade-off between the local NSD and the local FWHM at the center, 50 mm off-center and 100 mm off-center are shown in Fig. 7(a)–(c), where every 5 ML-EM iteration is plotted. The trade-off between the averaged NSD and the averaged FWHM is shown in Fig. 7(d). Reconstructed images and plots of FWHM at the same are shown in Figs. 8 and 9, averaged NSD level respectively. The numbers of ML-EM iterations are 40 (4-layer DOI), 41 (4-layer DOI with the DOIC), 50 (2-layer DOI) and 53 (non-DOI). In Fig. 7, the difference between 4-layer DOI and non-DOI results shows the improvement of image quality by using DOI information. Improved trade-off characteristics are obtained by 4-layer DOI at the off-center positions, while there is no remarkable advantage from using DOI information at the center. The trade-off results also indicate that the DOIC followed by the ML-EM has almost the same image quality as the ML-EM does. In Fig. 8, we see that almost uniform PSFs are obtained by using 4-layer DOI, while PSFs are blurred in the peripheral region in the 2-layer DOI and non-DOI cases. In the 4-layer DOI case, almost the same quality of image is obtained by the DOIC method. In all images, dark bands are seen on the uniform background at 100 mm off-center. We think that these artifacts appear because of the mismatched normalization. Fig. 9 shows that almost uniform radial and tangential FWHMs with better than 3 mm spatial resolution over the FOV are obtained by using 4-layer DOI information, while the ML-EM without DOI degrades radial resolution at the
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Finally, the ratios of computational cost of the ML-EM without DOI, the DOIC-ML-EM and the ML-EM with 4-layer DOI were 1, 3 and 16, respectively. For example, calculation time of one ML-EM iteration for the DOIC-ML-EM is 76 s on a Pentium 3.2 GHz single processor PC. In order to improve convergence, accelerated iterative algorithms such as ordered subsets methods should be used to replace the ML-EM. IV. CONCLUSION
Fig. 8. Reconstructed images using the ML-EM. (a) the ML-EM with 4-layer DOI, (b) the DOIC-ML-EM with 4-layer DOI, (c) the ML-EM with 2-layer DOI and (d) the ML-EM with non-DOI. 100 160 pixels are extracted and displayed from 250 250 pixels images.
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In this work, we developed a prototype system for the jPET-D4 which has a pair of detector blocks, and we evaluated the jPET-D4’s spatial resolution by line source measurements. First, radial spatial resolution of the jPET-D4 was estimated at 3.0 mm (center) and 4.1 mm (100 mm off-center) from a FBP reconstructed image. In the non-DOI case, radial resolution was degraded to 9.5 mm. Resolution uniformity was much improved by using 4-layer DOI information. Next, spatial resolution with the ML-EM image reconstruction was estimated at 2.1 mm (center) and 2.8 mm (100 mm off-center) and was improved by accurate system modeling. Trade-off characteristics between background noise and resolution were also investigated because improved spatial resolution is possible only when enhanced noise is avoided. Improved and stable trade-off characteristics were obtained by 4-layer DOI, while they were degraded at the off-center positions in the non-DOI case. The DOIC method, which was introduced to reduce computational cost to 1/5, was also applied to experimental data for the first time. We confirmed that the DOIC method retained the advantages of DOI information and accurate system modeling. Finally, 2-layer DOI information was not sufficient for this geometry to obtain uniform resolution, though resolution at the off-center was improved somewhat. These conclusions encourage us to continue the development of a real jPET-D4 scanner. ACKNOWLEDGMENT
Fig. 9. Radial and tangential FWHMs of the ML-EM reconstruction with 4-layer DOI, 2-layer DOI and non-DOI. The DOIC method was also applied to 4-layer DOI.
off-center positions. Compared with the FBP (Fig. 6), radial resolution is improved 30%–40% by the accurate system modeling we implemented. Taking into account the diameter of the line source, spatial resolution of the jPET-D4 is estimated at 2.1 mm (center) and 2.8 mm (100 mm off-center). The lines also show that the DOIC method is acceptable because spatial resolution is almost uniform though there is a slight resolution loss. Figs. 6 and Figs. 9 show that 2-layer DOI information is not sufficient for this geometry to obtain uniform resolution, though resolution at the off-center is improved somewhat.
The authors would like to thank Hamamatsu K. K., Japan, Hitachi Chemical Co., Japan, and Shimadzu Co., Japan. They would also like to thank Dr. H. Tsujii, Dr. S. Tanada, and Dr. M. Endo with NIRS for their encouragement, Mr. Y. Sato, Mr. Y. Ono, and Mr. M. Hamamoto with NIRS for their experimental assistance, and Mr. J. Y. Yeom with Tokyo University for the proofreading. REFERENCES [1] H. Murayama, H. Ishibashi, H. Uchida, T. Omura, and T. Yamashita, “Design of a depth of interaction detector with a PS-PMT for PET,” IEEE Trans. Nucl. Sci., vol. 47, no. 3, pp. 1045–1050, Jun. 2000. [2] N. Orita, H. Murayama, H. Kawai, N. Inadama, and T. Tsuda, “Threedimensional array of scintillation crystals with proper reflector arrangement for a depth of interaction detector,” IEEE Trans. Nucl. Sci., vol. 52, no. 1, pp. 8–14, Feb. 2005. [3] N. Hagiwara, T. Obi, T. Yamaya, M. Yamaguchi, N. Ohyama, K. Kitamura, H. Haneishi, and H. Murayama, “A performance study of the next generation PET using a new histogramming method for the DOI detector,” in IEEE Nucl. Sci. Symp. Med. Imag. Conf., 2003, M3-112.
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