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One way to speed-up iterative image reconstruction is by parallel computing with a computer cluster. However, as the number of computing threads increases, parallel efficiency decreases due to network transfer delay. In this paper, we proposed a method to reduce data transfer between computing threads by introducing an intra-thread update. The update factor is collected from each slave thread and a global image is updated as usual in the first K sub-iteration. In the rest of the sub-iterations, the global image is only updated at an interval which is controlled by a parameter L. In between that interval, the intra-thread update is carried out whereby an image update is performed in each slave thread locally. We investigated combinations of K and L parameters based on parallel implementation of RAMLA for the jPET-D4 scanner. Our evaluation used four workstations with a total of 16 slave threads. Each slave thread calculated a different set of LORs which are divided according to ring difference numbers. We assessed image quality of the proposed method with a hotspot simulation phantom. The figure of merit was the full-width-haft-maximum of hotspots and the background normalized standard deviation. At an optimum K and L setting, we did not find significant change in the output images. We also applied the proposed method to a Hoffman phantom experiment and found the difference due to intra-thread update was negligible. With the intra-thread update, computation time could be reduced by about 23%. Index Terms--Distributed computing, image reconstruction, positron emission tomography.

The jPET-D4 is a novel brain PET scanner which aims to achieve not only high spatial resolution but also high scanner sensitivity by using 4-layer depth-of-interaction (DOI) information. The dimensions of a system matrix for the jPET-D4 are 3.3 billion (lines-of-response) x 5 million (image elements) when a standard field-of-view (FOV) of 25 cm diameter is sampled with a [(1.5 mm).sup.3] voxel. The size of the system matrix is estimated as 117 petabytes (PB) with the accuracy of 8 bytes per element. An on-the-fly calculation is usually used to deal with such a huge system matrix. However we cannot avoid extension of the calculation time when we improve the accuracy of system modeling. In this work, we implemented an alternative approach based on pre-calculation of the system matrix. A histogram-based 3D OS-EM algorithm was implemented on a desktop workstation with 32 GB memory installed. The 117 PB system matrix was compressed under the limited amount of computer memory by (1) eliminating zero elements, (2) applying the DOI compression (DOIC) method and (3) applying rotational symmetry and an axial shift property of the crystal arrangement. Spanning, which degrades axial resolution, was not applied. The system modeling and the DOIC method, which had been validated in 2D image reconstruction, were expanded into 3D implementation. In particular, a new system model including the DOIC transformation was introduced to suppress resolution loss caused by the DOIC method. Experimental results showed that the jPET-D4 has almost uniform spatial resolution of better than 3 mm over the FOV. Finally the first human brain images were obtained with the jPET-D4. Index Terms--Depth-of-interaction (DOI), positron emission tomography (PET), system modeling, 3D image reconstruction.

In a conventional PET scanner, coincidence events are limited by the energy window for detection of photoelectric events. In contrast, Compton scatter events occur both in a patient and in detector crystals. Scatter events within the patient cause scatter coincidences, but scatter events within crystals have useful information for an activity distribution. The PET scanner with an extended energy window has higher sensitivity but higher scatter fraction than the PET scanner with a default energy window. In this work, we develop a scatter reduction method using a depth-of-interaction (DOI) detector. The DOI detector can make an upper layer act as an absorber of patient scatter, thus shielding a lower layer. Therefore, Compton scatter events with an interaction at the lower layer mainly have more crystal scatter events than patient scatter events. Our method proposes a different energy window for each layer. The energy window of the upper layer is limited to the region of photopeak events, the same as done for the conventional PET scanner. The energy window of the lower layer is extended to the region of crystal scatter events and photopeak events. We tested our proposed technique for a whole-body PET scanner using GATE simulations. Simulation results show the DOI-PET scanner can provide more true events while keeping a low scatter fraction using our scatter reduction method. We conclude this method is promising for obtaining high image quality using DOI information and energy information. Index Terms--DOI, energy window, PET.

An 8-layer depth of interaction (DOI) detector was designed based on the technique we have developed for 4-layer DOI detectors. The new detector achieves 8-layer DOI encoding by pulse shape discrimination (2-layer DOI encoding) and an optimized reflector arrangement in a 3-dimensional crystal array (4-layer DOI encoding). Its capability was proved with an 8-layer 10 x 10 [Gd.sub.2] Si[O.sub.5] (GSO) crystal array coupled to a 256-channel flat panel position sensitive photomultiplier tube (256ch FP-PMT). The dimensions of each crystal element were 2.90 mm x 2.90 mm x 3.75 mm and the interval between 16 x 16 multi anodes in the 256ch FP-PMT was 3.04 mm. Two different dopant concentrations in GSO were chosen for pulse shape discrimination: GSO crystals of 0.5 mol% and 1.5 mol% Ce dopant that have 60 ns and 35 ns scintillation decay times, respectively. In the crystal array, Layer-l, the farthest from the 256ch FP-PMT, and Layers-3, -5 and -7 were composed of GSO crystals of 0.5 mol% Ce dopant. All other layers were composed of GSO crystals of 1.5 mol% Ce dopant. Performance of the 8-layer DOI detector was evaluated by irradiating with 662 keV uniform gamma-rays and the capability was judged to be good. To prove the validity of the layer encoding, a fan-beam of 662 keV gamma-rays was irradiated onto the side face of each layer. The obtained 2-dimensional position histograms showed the right structure in each corresponding layer clearly. Light output uniformity among DOI layers and energy resolutions were measured on the pulse height distributions of the central crystal in each layer. The crystals in Layer-2 and Layer-3 showed the smallest light output and their full energy peak channels were 62% to the largest peak channel of the Layer-8 crystal distribution. Energy resolutions were about 15% for all eight layers. Index Terms--Depth of interaction (DOI), GSO, positron emission tomography (PET).

We found that [Bi.sub.4] [Ge.sub.3] [O.sub.12] (BGO) scintillator can be elements of a four-layer depth of interaction (DOI) detector and it was proved with a 12 x 12 x 4 array of BGO crystals in dimensions of 2.9 mm x 2.9 mm x 7.5 mm coupled to a 256-channel flat panel position sensitive photomultiplier tube. Appropriate reflector insertion in the array makes all crystal identification possible on one position histogram. Despite the large refractivity and small light output of BGO, the four-layer BGO detector showed no significant variation in the full energy peaks among all crystal elements. When no optical grease was used in the construction of the BGO DOI-block and irradiated with gamma-rays from [sup.137]Cs, a top layer crystal has 80% of light output relative to the bottom layer. The obtained two-dimensional position histogram by the irradiation was clear enough to allow identification of the crystals of interaction. Profiles of the histogram show peak-to-valley ratio of 1.9:1 for the top layer crystals and larger ratio for other layer crystals in the experiment. Index Terms--BGO, depth of interaction (DOI), positron emission tomography (PET).

Previously, we proposed a new depth of interaction (DOI) encoding method and proved that it worked successfully with four-layered [Gd.sub.2]Si[O.sub.5] crystals for a small animal positron emission tomography (PET) detector. We are now planning to develop a small animal PET scanner, jPET-RD (for rodents with DOI detectors), which has both high resolution and high sensitivity by the use of a DOI detector with a 32 x 32 x 4 crystal array. The scintillator for the detector will be [Lu.sub.2(1-x)][Y.sub.2x]Si[O.sub.5] (LYSO). In this work, we evaluated performance of a DOI detector composed of four layers of a 12 x 12 LYSO (Lu: 98%, Y: 2%) crystal array by irradiating 511 keV gamma rays uniformly. The new encoding method was used for crystal identification. The size of each crystal was 1.46 mm x 1.46 mm x 4.5 mm. The crystal block was coupled to a 256-channel flat panel position sensitive photomultiplier tube, which has 16 x 16 multi anodes at intervals of 3.04 mm. As we expected, all crystals are expressed on a single two-dimensional position histogram without overlapping. Energy resolution of all events is 21.8% and time resolution of all events is 0.69 ns in FWHM. When layers are counted from the top, the energy resolutions of the first, second, third, and fourth layer events are 11.6%, 12.3%, 13.3%, and 19.1% and the time resolutions are 0.60 ns, 0.59 ns, 0.60 ns, and 0.66 ns, respectively. Index Terms--Positron emission tomography (PET), depth of interaction (DOI), small animal study, scintillation detector.

This paper describes a depth-of-interaction recognition method that can be applied to radiation detectors for positron emission tomography. The proposed method uses optical filters to differentiate wavelength distribution of scintillation photons depending on crystal depth positions. Then the crystal of interaction can be identified with a multianode photodetector whose sensitive surface is partly covered with optical filters. A validation experiment was performed with a position sensitive photomultiplier. As a result, it was proved that the crystal depth of interaction was clearly identified for photoabsorption events. Index Terms--Biomedical applications of nuclear radiation, nuclear imaging, positron emission tomography, scintillation detector.

A new method to acquire four-layer depth of interaction (DOI) information is proposed for the next generation positron emission tomography scanner (jPET-D4) that realizes high resolution and high sensitivity. The detector module of the jPET-D4 is a 16 x 16 x 4 [Gd.sub.2]Si[O.sub.5]: Ce (GSO) multicrystal array coupled with a 256 ch flat panel position sensitive photomultiplier tube (256 ch FP-PMT) having large opening area. The first challenge to encode DOI information was carried out with 8 x 8 array of units consisted of 2 x 2 x 4 crystal elements. The unit is developed for four-layer DOI encoding in previous report. Its crystal identification performance is evaluated by uniform gamma ray irradiation. The measured scintillation events are mapped on a two-dimensional (2-D) position histogram according to the relative ratio of the multianode output of the FP-PMT. However, peaks corresponding to the crystal elements of one unit form a colony in the resultant 2-D position histogram and there is large space between adjacent colonies. In the new method, the reflector arrangement which makes proper light sharing in the multicrystal array decreases such wasted space. Consequently, peak-to-valley on the 2-D position histogram was improved to 3.3:1 from 1.8:1. We found energy performance was also enhanced by the new method. Index Terms--Depth of interaction (DOI), nuclear medicine, positron emission tomography (PET), scintillation detector.

A 256 channel flat panel position sensitive photomultiplier tube (256ch FP-PMT) was evaluated for application to a depth of interaction (DOI) PET detector composed of small crystal elements. The 256ch FP-PMT has 52 x 52 mm opening area with 89% useful area. Its 256 anodes are placed at a 3.04 mm interval. To estimate the FP-PMT performance, light spread functions of anodes at central and peripheral regions of a prototype 256ch FP-PMT were measured with a [Gd.sub.2]Si[O.sub.5] (GSO) crystal sized 1.42 x 1.42 x 4.5 mm. The crystal cross section area is about one quarter of one anode area of the FP-PMT. It was found that light spread functions of peripheral anodes were similar to the functions of central anodes and also the functions measured with a 2.9 x 2.9 x 7.5 mm GSO crystal which has almost the same dimensions of cross-section as the anode area. Transit time fluctuation among the 256ch FP-PMT anodes was estimated by measuring time resolutions of a LuYSi[O.sub.5] (LYSO) crystal at some central and peripheral positions. The LYSO crystal has the same dimensions as the smaller GSO crystal. Ba[F.sub.2] was used for a reference detector. The obtained distributions show about the same time resolution between the central and peripheral positions and the full width at half maximum is (366 [+ or -] 15) ps. The transit time fluctuation is [+ or -] 106 ps. Two-dimensional position histograms of a 32 x 32 GSO crystal array and two layers of 9 x 9 GSO crystal arrays are obtained by uniform gamma-ray irradiation. The crystal dimensions are 1.42 x 1.42 x 4.5 mm so that the 32 x 32 array covers all the useful area and indicates variation of crystal identification performance over the useful area. The 9 x 9 x 2 array is coupled to peripheral region. The resultant histograms confirm that a 256ch FP-PMT has enough capability for identifying crystals of this size even on the periphery and in DOI arrangement. Index Terms--Multi-anode photomultiplier tube (PMT), position sensitive detector, scintillation detector, small animal positron emission tomography (PET).

A depth of interaction detector is developed for the next generation of positron emission tomography (PET) scanners. The detector unit consists of 8 x 8 crystal blocks with four layers of 2 x 2 [Gd.sub.2]Si[O.sub.5]:Ce arrays coupled to a 52 mm square position sensitive photomultiplier tube (PS-PMT). Each scintillation event is mapped in a two-dimensional (2-D) position histogram through the relative ratio of the output signals of the PS-PMT. To facilitate high spatial resolution imaging, accurate crystal identification is needed. A statistical model based on the approach of a Gaussian mixture model (GMM) is introduced for crystal identification. In the GMM, a cluster center and range attributed to individual peaks in the 2-D position histogram are defined. GMM can simultaneously estimate overlapping regions projected each crystal element. After block separation of 8 x 8 on the 2-D distribution, the crystal element regions are identified by the GMM in each block. The GMM method is applied two times, once for the cluster centers and once for determination of the range. These results are used to generate a look-up-table (LUT). This method successfully identified all crystal elements in the clustering area. By Monte Carlo simulation, we also proved that GMM method could choose LUT patterns to high resolution or high sensitivity with one parameter. Index Terms--Crystal identification, depth of interaction (DOI), Gaussian mixture model (GMM), positron emission tomography (PET), position sensitive photomultiplier tube.

We are now planning to develop a positron emission tomograph dedicated to small animals, such as rats and mice, which meets the demand for higher sensitivity. For the positron emission tomography (PET), we newly designed a four-layer depth of interaction (DOI) detector, which is constructed of all the same crystal elements. In this DOI detector, appropriate insertion of the reflector controls the behavior of scintillation photons by inserting the reflectors between crystal elements so that the DOI information of four layers can be extracted from one two-dimensional (2-D) position histogram made by Anger-type calculation. As a preliminary experiment, we measured crystal identification performance of the DOI detector, which consists of four layers of a 16 x 16 crystal array using [Gd.sub.2]Si[O.sub.5] crystals with Ce concentration of 0.5 mol %. Each crystal is in dimensions of 1.42 mm x 1.42 mm x 4.5 mm. A crystal block is optically coupled to a 256-channel flat panel position sensitive photomultiplier tube whose opening area is 52.0 mm x 52.0 mm. We obtained sufficient positioning performance for this four-layer DOI detector on the 2-D position histogram. We concluded that it would be a promising device to realize a small animal PET scanner with high sensitivity and high resolution. Index Terms--Depth of interaction, positron emission tomography (PET), small animal study.

A 256ch flat panel position sensitive photomultiplier tube (FP-PMT) is a promising device for a PET detector because of its large opening area, 52 mm x 52 mm, and small dead space. The useful area of the 256ch FP-PMT is 89% to the opening area. The 256ch FP-PMT contains 16 x 16 matrix anodes with 3.04 mm intervals between them so that the 256ch FP-PMT affords optical coupling with a 16 x 16 array of scintillation crystals having 3 mm x 3 mm bottom area. Its 14.7 mm thickness will also ensure a compact volume and less weight for the PET apparatus. Using a prototype 256ch FP-PMT, we measured light spread function of a central anode and crystal identification ability with 2.9 mm x 2.9 mm x 7.5 mm [Gd.sub.2]Si[O.sub.5] (GSO) crystals. The full width at half maximum of the light spread function was found to be 4.6 mm. As regards positioning performance, the resultant positioning image map assures its capability for crystal identification in a 16 x 16 array of the GSO crystals. For the use of a 256ch FP-PMT having a large useful area, we made a new proposal for easier construction of an array with many crystal elements. The way utilizing multi-layer polymer mirrors, a reflector, properly processed by laser can be applied to other various shaped detectors. Index Terms--Multi-anode PMT, position sensitive detector, positron emission tomography (PET), scintillation detector.

As part of the next generation PET project, uniformity of full energy pulse height for all crystal elements was improved in the depth of interaction (DOI) detector constructed of three-dimensional crystal arrays. In our previous report, we found that the DOI detector constructed of four stages of a 2 x 2 [Gd.sub.2]Si[O.sub.5]:Ce (GSO) crystal array provides good crystal identification performance but poor uniformity of the energy pulse height distribution. The upper stage crystal elements which stay further from the photocathode of a PMT have a tendency to show lower energy pulse height. For example, the ratio of the full energy peak of the top stage crystal to the bottom stage one was about 0.3. We designed a new DOI detector improved in the uniformity. By optimizing crystal surface finishes, reflector configurations, and optical coupling between crystal elements, we got comparable energy pulse height from the upper stage crystals to the bottom stage crystals. Despite this change of detector conditions, good separation between each area corresponding to crystal elements is maintained on two-dimensional histograms obtained by Anger-type position calculation. The uniform full energy pulse height of every stage crystal allows a narrower dynamic range of the electrical circuits, and may give a great advantage in getting an accurate scatter correction. It also improves energy and timing resolution. Index Terms--Depth of interaction, nuclear medicine, positron emission tomography (PET), scintillation detector.

A high-performance positron emission tomography (PET) scanner, which measures depth-of-interaction (DOI) information, is under development at the National Institute of Radiological Sciences in Japan. Image reconstruction methods with accurate modeling of the system response functions have been successfully used to improve PET image quality. It is, however, difficult to apply these methods to the DOI-PET scanner because the dimension of DOI-PET data increases in proportion to the square of the number of DOI layers. In this paper, we propose a compressed imaging system model for DOI-PET image reconstruction, in order to reduce computational cost while keeping image quality. The basic idea of the proposed method is that the DOI-PET imaging system is highly redundant. First, DOI-PET data is transformed into compact data so that data bins with highly correlating sensitivity functions are combined. Then image reconstruction methods based on accurate system modeling, such as the maximum likelihood expectation maximization (ML-EM), are applied. The proposed method was applied to simulated data for the DOI-PET scanner operated in 2-D mode. Then the tradeoff between the background noise and the spatial resolution was investigated. Numerical simulation results show that the proposed method followed by ML-EM reduces computational cost effectively while keeping the advantages of the accurate system modeling and DOI information. Index Terms--Depth-of-interaction (DOI), imaging system model, maximum likelihood expectation maximization (ML-EM), positron emission tomography, statistical image reconstruction.

We have estimated count rate properties of thrree--dimensional (3-D) positron emission tomography (PET) scanners based on a [Gd.sub.2]Si[O.sub.5]: Ce (GSO) detector with depth of interaction (DOI) capability using a large-area position-sensitive photomultiplier tube (PS-PMT). The proposed detector unit consists of 64 crystal blocks with four stages of 2 x 2 GSO arrays coupled to a 52-mm square PS-PMT which has small dead space. With appropriate light control in the crystal block, DOI information can be obtained using simple Anger-type positioning logic. Thus, dead-time factors can be calculated using a count rate model with standard acquisition architecture. Compton and photoelectric interactions in the scintillator and uniform cylindrical phantoms were tracked by Monte Carlo simulation programs. Since the DOI detector can provide high resolution throughout the entire field of view, 3-D PET scanners with a large solid angle covered by the detectors with relatively small ring diameters were simulated. The preliminary results suggest that, compared to current PET scanners, high noise equivalent count rate can be obtained by the proposed scanner designs despite the relatively large size of the detector module. The count rate performance can be improved by the reduction of single events that cause block dead-time losses at the cost of a slight decrease in sensitivity. Index Terms--Count rate performance, depth of interaction (DOI), Monte Carlo simulation, positron emission tomography (PET).

We report the usefulness of coarse septa in positron emission tomography (PET) by Monte Carlo simulation. Coarse septa result in higher sensitivity than found with the two-dimensional mode with conventional full septa and lower scatter fraction than the three-dimensional mode without septa. We propose a new scatter correction method using coarse septa, where scatter components are estimated from coincidence data for those line-of-responses that are intercepted by the coarse septa. This scatter correction potentially has the ability to cope with scatter from radioactivity outside the field of view. In addition, we show the feasibility of a lead tungstate (PWO) PET scanner with coarse septa. Index Terms--Coarse septa, lead tungstate, Monte Carlo method, positron emission tomography (PET), scatter correction.

A new method for a four-stage depth of interaction (DOI) detector is proposed. The four-stage DOI detector is constructed with two kinds of [Gd.sub.2] Si[O.sub.5]: Ce (GSO) crystals doped with different amounts of Ce, 0.5 mol% and 1.5 mol%. The amount of Ce in GSO determines the scintillation decay time constant, and it is 60 ns for the 0.5 mol% GSO and 35 ns for 1.5 mol% GSO. This difference led to the introduction of pulse-shape discrimination, which would distinguish between two kinds of event data from respective GSOs and sort them into two groups. By independently applying Anger-type position arithmetic to the data of each group, two two-dimensional (2-D) histograms are obtained. The crystal of interaction can be identified on these histograms in which only 0.5 mol% or 1.5 mol% GSO crystal elements are expressed. To evaluate this method, we constructed the four-stage DOI detector by alternately stacking 1.5 mol% GSO crystal stages and 0.5 mol% stages. The result of a scanning measurement with a [sup.137]Cs gamma-ray beam proved that the DOI detector had enough accuracy in crystal identification. Index Terms--Depth of interaction, gadolinium orthosilicate, positron emission tomography (PET), pulse-shape discrimination.

Algebraic reconstruction methods have been successfully used to improve quality of positron emission tomography (PET) images by accurate modeling of measurement system, but they have computational burden. We propose a fast PET image reconstruction method based on an algebraic technique. In this method, reconstruction operators are pre-computed approximately using subsets of sensitivity functions. The subsets contain the sensitivity functions that contribute significantly to each point to be reconstructed. The proposed method was applied to simulated data and experimental data for the ECAT EXACT HR+ (Siemens/CTI) scanner operating in 2D mode. These results show that the proposed method produces images with almost the same quality as the conventional algebraic methods do and has a similar computation time to the filtered backprojection method.