cMiCE Detector Research Articles

A machine learning method for fast and accurate characterization of depth-of-interaction gamma cameras

Measuring the depth-of-interaction (DOI) of gamma photons enables increasing the resolution of emission imaging systems. Several design variants of DOI-sensitive detectors have been recently introduced to improve the performance of scanners for positron emission tomography (PET). However, the accurate characterization of the response of DOI detectors, necessary to accurately measure the DOI, remains an unsolved problem. Numerical simulations are, at the state of the art, imprecise, while measuring directly the characteristics of DOI detectors experimentally is hindered by the impossibility to impose the depth-of-interaction in an experimental set-up. In this article we introduce a machine learning approach for extracting accurate forward models of gamma imaging devices from simple pencil-beam measurements, using a nonlinear dimensionality reduction technique in combination with a finite mixture model. The method is purely data-driven, not requiring simulations, and is applicable to a wide range of detector types. The proposed method was evaluated both in a simulation study and with data acquired using a monolithic gamma camera designed for PET (the cMiCE detector), demonstrating the accurate recovery of the DOI characteristics. The combination of the proposed calibration technique with maximum- a posteriori estimation of the coordinates of interaction provided a depth resolution of ≈1.14 mm for the simulated PET detector and ≈1.74 mm for the cMiCE detector. The software and experimental data are made available at http://occiput.mgh.harvard.edu/depthembedding/.

Experimental validation of improved 3D SBP positioning algorithm in PET applications using UW Phase II Board

Continuous scintillator-based detectors have been considered as a competitive and cheaper approach than highly pixelated discrete crystal positron emission tomography (PET) detectors, despite the need for algorithms to estimate 3D gamma interaction position. In this work, we report on the implementation of a positioning algorithm to estimate the 3D interaction position in a continuous crystal PET detector using a Field Programmable Gate Array (FPGA). The evaluated method is the Statistics-Based Processing (SBP) technique that requires light response function and event position characterization. An algorithm has been implemented using the Verilog language and evaluated using a data acquisition board that contains an Altera Stratix III FPGA. The 3D SBP algorithm was previously successfully implemented on a Stratix II FPGA using simulated data and a different module design. In this work, improvements were made to the FPGA coding of the 3D positioning algorithm, reducing the total memory usage to around 34%. Further the algorithm was evaluated using experimental data from a continuous miniature crystal element (cMiCE) detector module. Using our new implementation, average FWHM (Full Width at Half Maximum) for the whole block is 1.71±0.01mm, 1.70±0.01mm and 1.632±0.005mm for x, y and z directions, respectively. Using a pipelined architecture, the FPGA is able to process 245,000 events per second for interactions inside of the central area of the detector that represents 64% of the total block area. The weighted average of the event rate by regional area (corner, border and central regions) is about 198,000 events per second. This event rate is greater than the maximum expected coincidence rate for any given detector module in future PET systems using the cMiCE detector design.

Multiplexing strategies for monolithic crystal PET detector modules

To reduce the number of output channels and associated cost in PET detectors, strategies to multiplex the signal channels have been investigated by several researchers. This work aims to find an optimal multiplexing strategy for detector modules consisting of a monolithic LYSO scintillator coupled to a 64-channel PMT.We apply simulated multiplexing strategies to measured data from two continuous miniature crystal element (cMiCE) detector modules. The strategies tested include standard methods such as row column summation and its variants, as well as new data-driven methods involving the principal components of measured data and variants of those components. The detector positioning resolution and bias are measured for each multiplexing strategy and the results are compared.The mean FWHM over the entire detector was 1.23 mm for no multiplexing (64 channels). Using 16 principal component channels yielded a mean FWHM resolution of 1.21 mm, while traditional row/column summation (16 channels) yielded 1.28 mm. Using 8 principal component output channels resulted in a resolution of 1.30 mm.Using the principal components of the calibration data to guide the multiplexing scheme appears to be a viable method for reducing the number of output data channels. Further study is needed to determine if the depth-of-interaction resolution can be preserved with this multiplexing scheme.

Performance Evaluation of Small Animal PET Scanners With Different System Designs

This study evaluated the image quality metrics of small animal PET scanners based upon measured single detector module positioning performance. A semi-analytical approach was developed to study PET scanner performance in the scenario of multiple realizations. Positron range blurring, scanner system response function (SRF) and statistical noise were included in the modeling procedure. The scanner sensitivity map was included in the system matrix during maximum likelihood expectation maximization (MLEM) reconstruction. Several image quality metrics were evaluated for octagonal ring PET scanners consisting of continuous miniature crystal element (cMiCE) detector modules with varying designs. These designs included 8 mm and 15 mm thick crystal detectors using conventional readout with the photosensors on the exit surface of the crystal and a 15 mm thick crystal detector using our proposed sensor-on-the-entrance (SES) design. For the conventional readout design, the results showed that there was a tradeoff between bias and variance with crystal thickness. The 15 mm crystal detector had better detection task performance, while quantitation task performance was degraded. On the other hand, our SES detector had similar detection efficiency as the conventional design using a 15 mm thick crystal and had similar intrinsic spatial resolution as the conventional design using an 8 mm thick crystal. The end result was that by using the SES design, one could improve scanner quantitation task performance without sacrificing detection task performance.

Use of Cramer-Rao Lower Bound for Performance Evaluation of Different Monolithic Crystal PET Detector Designs.

We have previously reported on continuous miniature crystal element (cMiCE) PET detectors that provide depth of interaction (DOI) positioning capability. A key component of the design is the use of a statistics-based positioning (SBP) method for 3D event positioning. The Cramer-Rao lower bound (CRLB) expresses limits on the estimate variances for a set of deterministic parameters. We examine the CRLB as a useful metric to evaluate the performance of our SBP algorithm and to quickly compare the best possible resolution when investigating new detector designs.In this work, the CRLB is first reported based upon experimental results from a cMiCE detector using a 50×50×15-mm(3) LYSO crystal readout by a 64-channel PMT (Hamamatsu H8500) on the exit surface of the crystal. The X/Y resolution is relatively close to the CRLB, while the DOI resolution is more than double the CRLB even after correcting for beam diameter and finite X (i.e., reference DOI position) resolution of the detector. The positioning performance of the cMiCE detector with the same design was also evaluated through simulation. Similar with the experimental results, the difference between the CRLB and measured spatial resolution is bigger in DOI direction than in X/Y direction.Another simulation study was conducted to investigate what causes the difference between the measured spatial resolution and the CRLB. The cMiCE detector with novel sensor-on-entrance-surface (SES) design was modeled as a 49.2×49.2×15-mm(3) LYSO crystal readout by a 12×12 array of 3.8×3.8-mm(2) silicon photomultiplier (SiPM) elements with 4.1-mm center-to-center spacing on the entrance surface of the crystal. The results show that there are two main causes to account for the differences between the spatial resolution and the CRLB. First, Compton scatter in the crystal degrades the spatial resolution. The DOI resolution is degraded more than the X/Y resolution since small angle scatter is preferred. Second, our maximum likelihood (ML) clustering algorithm also has limitations when developing 3D look up tables during detector calibration.

Resolution Properties of a Prototype Continuous Miniature Crystal Element (cMiCE) Scanner.

Continuous miniature crystal element (cMiCE) detectors are a potentially lower cost alternative for high resolution discrete crystal PET detector designs. We report on performance characteristics of a prototype PET scanner consisting of two cMiCE detector modules. Each cMiCE detector is comprised of a 50 × 50 × 8 mm3 LYSO crystal coupled to a 64 channel multi-anode PMT. The cMiCE detectors use a statistics-based positioning method based upon maximum likelihood estimation for event positioning. By this method, cMiCE detectors can also provide some depth of interaction event positioning information. For the prototype scanner, the cMiCE detectors were positioned across from one another on a horizontal gantry with a detector spacing of 10.7 cm. Full tomographic data were collected and reconstructed using single slice rebinning and filtered back projection with no smoothing. The average image resolutions in X (radial), Y (transverse) and Z (axial) were 1.05 ± 0.08 mm, 0.99 ± 0.07 mm, 1.24 ± 0.31 mm FWHM. These initial imaging results from a prototype imaging system demonstrate the outstanding image resolution performance that can be achieved using the potentially lower cost cMiCE detectors.

Design of a Real Time FPGA-Based Three Dimensional Positioning Algorithm

We report on the implementation and hardware platform of a real time Statistics-Based Positioning (SBP) method with depth of interaction processing for a positron emission tomography detector. The processing method works in conjunction with continuous miniature crystal element (cMiCE) detectors using a sensor on the entrance surface design. Our group previously reported on a Field Programmable Gate Array (FPGA) SBP implementation that provided a two dimensional (2D) detector positioning solution . This new implementation extends that work to take advantage of three dimensional (3D) look up tables to provide a 3D positioning solution that improves intrinsic spatial resolution. Resolution is most improved along the edges of the crystal, an area where the 2D algorithm's performance suffers. The algorithm allows an intrinsic spatial resolution of ~ 0.90 mm FWHM in X and Y and a resolution of ~ 1.90 mm FWHM in Z (i.e., the depth of the crystal) based upon DETECT2000 simulation results that include the effects of Compton scatter in the crystal. A pipelined FPGA implementation is able to process events in excess of 220 K events per second, which is greater than the maximum expected coincidence rate for an individual detector. In contrast to all detectors being processed at a centralized host (as in the current system) a separate FPGA is available at each detector, thus dividing the computational load. A prototype design has been implemented and tested on an Altera Stratix II FPGA using a reduced word size due to memory limitations of our commercial prototyping board.

Calibration Procedure for a Continuous Miniature Crystal Element (cMiCE) Detector

We report on methods to speed up the calibration process for a continuous miniature crystal element (cMiCE) detector. Our cMiCE detector is composed of a 50-mm by 50-mm by 8-mm-thick monolithic LYSO crystal coupled to a 64-channel, flat-panel photomultiplier tube (PMT). It achieves an average intrinsic spatial resolution of ~1.4 mm full width at half maximum (FWHM) over the useful face of the detector through the use of a statistics-based positioning algorithm. A drawback to the design is the length of time it takes to calibrate the detector. We report on three methods to speed up this process. The first method is to use multiple point fluxes on the surface of the detector to calibrate different points of the detector from a single data acquisition. A special multisource device that can produce up to 16 point fluxes has been custom designed for this purpose. The second scheme is to characterize the detector with coarser sampling and use interpolation to create lookup tables with the desired detector binning (e.g., 0.253 mm). The intrinsic spatial resolution performance was investigated for sampling intervals of 1.013, 2.026, 3.039, and 4.052 mm. The third method is to adjust the point flux diameter by varying the geometry of the setup. A larger point flux diameter will increase the coincidence counting rate. The average intrinsic spatial resolution was 1.38 mm FWHM using four point fluxes, 1.013 mm detector sampling, and ~0.5 mm point flux on the surface of the detector. The average intrinsic spatial resolution increased slightly to 1.45 mm FWHM when using 16 point fluxes with a detector sampling of 3.039 mm. Adjusting the point flux size degraded the intrinsic spatial resolution the most (~9%) and provided the smallest speed up factor. In conclusion using 16 point fluxes and a sampling interval of 3.039 mm, the characterization time for a cMiCE detector can be reduced by a factor of 144 with minimal impact on the intrinsic spatial resolution of the detector.

Design of an FPGA-Based Algorithm for Real-Time Solutions of Statistics-Based Positioning

We report on the implementation of an algorithm and hardware platform to allow real-time processing of the statistics-based positioning (SBP) method for continuous miniature crystal element (cMiCE) detectors. The SBP method allows an intrinsic spatial resolution of ~1.6 mm FWHM to be achieved using our cMiCE design. Previous SBP solutions have required a postprocessing procedure due to the computation and memory intensive nature of SBP. This new implementation takes advantage of a combination of algebraic simplifications, conversion to fixed-point math, and a hierarchal search technique to greatly accelerate the algorithm. For the presented seven stage, 127 × 127 bin LUT implementation, these algorithm improvements result in a reduction from >7 × 10(6) floating-point operations per event for an exhaustive search to < 5 × 10(3) integer operations per event. Simulations show nearly identical FWHM positioning resolution for this accelerated SBP solution, and positioning differences of <0.1 mm from the exhaustive search solution. A pipelined field programmable gate array (FPGA) implementation of this optimized algorithm is able to process events in excess of 250 K events per second, which is greater than the maximum expected coincidence rate for an individual detector. In contrast with all detectors being processed at a centralized host, as in the current system, a separate FPGA is available at each detector, thus dividing the computational load. These methods allow SBP results to be calculated in real-time and to be presented to the image generation components in real-time. A hardware implementation has been developed using a commercially available prototype board.

New Continuous Miniature Crystal Element (cMiCE) Detector Geometries.

Continuous miniature crystal element (cMiCE) detectors are a potentially lower cost alternative to high resolution discrete crystal designs. We report on the intrinsic spatial resolution performance for two cMiCE PET detector designs with depth of interaction (DOI) positioning capability. The first detector utilizes a 50 mm by 50 mm by 8 mm LYSO crystal coupled to a 64 channel, multi-anode PMT. It provides 4 layers of DOI information. The crystal has beveled edges along two of its sides to improve the detector packing when placed in a ring geometry. The second detector utilizes a 50 mm by 50 mm by 15 mm, rectangular LYSO crystal coupled to a 64 channel, multi-anode PMT. It provides up to 15 layers of DOI information. The average intrinsic X, Y spatial resolution for the 8 mm thick, truncated crystal detector was 1.33 +/- 0.31 mm FWHM (45.6 mm by 46.6 mm useful imaging area). The average DOI resolution was 3.5 +/- 0.22 mm. The average intrinsic X, Y spatial resolution for the 15 mm thick crystal detector was 1.74 +/- 0.35 mm FWHM (44.6 mm by 44.6 mm useful imaging area). In addition, the average DOI spatial resolution for 56 test points spanning a 26.4 mm by 12.2 mm region of the crystal was 4.80 +/- 0.36 mm. We believe the 8 mm thick truncated crystal design is suitable for mouse imaging while the 15 mm thick crystal design is more suited for human organ specific imaging systems (e.g., breast and brain).

Parametric positioning of a continuous crystal PET detector with depth of interaction decoding

Here we demonstrate a parametric positioning method on a continuous crystal detector. Three different models for the light distribution were tested. Diagnosis of the residues showed that the parametric model fits the experimental data better than Gaussian and Cauchy models in our particular experimental setup. Based on the correlation between the spread and the peak value of the light distribution model with the depth of interaction (DOI), we were able to estimate the three-dimensional position of a scintillation event. On our continuous miniature crystal element (cMiCE) detector module with 8 mm thick LYSO crystal, the intrinsic spatial resolution is 1.06 mm at the center and 1.27 mm at the corner using a maximum-likelihood estimation (MLE) method and the parametric model. The DOI resolution (full width at half maximum) is estimated to be ∼3.24 mm. The positioning method using the parametric model outperformed the Gaussian and Cauchy models, in both MLE and weighted least-squares (WLS) fitting methods. The key feature of this technique is that it requires very little calibration of the detector, but still retains high resolution and high sensitivity.

Depth of interaction decoding of a continuous crystal detector module

We present a clustering method to extract the depth of interaction (DOI) information from an 8 mm thick crystal version of our continuous miniature crystal element (cMiCE) small animal PET detector. This clustering method, based on the maximum-likelihood (ML) method, can effectively build look-up tables (LUT) for different DOI regions. Combined with our statistics-based positioning (SBP) method, which uses a LUT searching algorithm based on the ML method and two-dimensional mean–variance LUTs of light responses from each photomultiplier channel with respect to different gamma ray interaction positions, the position of interaction and DOI can be estimated simultaneously. Data simulated using DETECT2000 were used to help validate our approach. An experiment using our cMiCE detector was designed to evaluate the performance. Two and four DOI region clustering were applied to the simulated data. Two DOI regions were used for the experimental data. The misclassification rate for simulated data is about 3.5% for two DOI regions and 10.2% for four DOI regions. For the experimental data, the rate is estimated to be ∼25%. By using multi-DOI LUTs, we also observed improvement of the detector spatial resolution, especially for the corner region of the crystal. These results show that our ML clustering method is a consistent and reliable way to characterize DOI in a continuous crystal detector without requiring any modifications to the crystal or detector front end electronics. The ability to characterize the depth-dependent light response function from measured data is a major step forward in developing practical detectors with DOI positioning capability.

Performance Comparisons of Continuous Miniature Crystal Element (cMiCE) Detectors

In this paper, we investigated the performance characteristics of continuous miniature crystal element (cMiCE) detectors. Versions with a 25 mm by 25 mm by 4 mm-thick LSO crystal and with a 50 mm by 50 mm by 8 mm-thick LYSO crystal were evaluated. Both detectors utilize a 64-channel flat panel photomultiplier tube (PMT). The intrinsic spatial resolution for the detectors was evaluated using Anger (i.e., simple centroid) positioning and a statistics based positioning (SBP) algorithm. We also compared the intrinsic spatial resolution for the 8-mm-thick LYSO crystal using different reflective materials (e.g., TFE Teflon, white paint, and a polymer mirror film) applied on the entrance surface of the crystal. The average energy resolution was 20% for the 4-mm-thick LSO crystal and ranged from 16% to 21%, depending upon reflective material, for the 8-mm-thick LYSO crystal. The average intrinsic spatial resolution for the 4-mm-thick crystal was 1.8-mm full width at half maximum (FWHM) for Anger positioning to within 3 mm of the crystal's edge and 1.14-mm FWHM for SBP to within 2 mm of the edge. The average intrinsic spatial resolution for the 8-mm-thick crystal was 2.2-mm FWHM for Anger positioning to within 8 mm of the crystal's edge and 1.3- to 1.5-mm FWHM (depending on reflective material used) for SBP to within 2 mm of the edge. Intrinsic spatial resolution is reported without correcting for point source size. The point spot flux had a FWHM of about 0.52 mm. The SBP algorithm resulted in significant improvement in intrinsic spatial resolution, linearity of positioning result, and effective field of view (FOV) for our cMiCE detector

CMiCE: a high resolution animal PET using continuous LSO with a statistics based positioning scheme

Objective: Detector designs for small animal scanners are currently dominated by discrete crystal implementations. However, given the small crystal cross-sections required to obtain very high resolution, discrete designs are typically expensive, have low packing fraction, reduced light collection, and are labor intensive to build. To overcome these limitations we have investigated the feasibility of using a continuous miniature crystal element (cMiCE) detector module for high resolution small animal PET applications. Methods: The detector module consists of a single continuous slab of LSO, 25×25 mm 2 in exposed cross-section and 4 mm thick, coupled directly to a PS-PMT (Hamamatsu R5900-00-C12). The large area surfaces of the crystal were polished and painted with TiO 2 and the short surfaces were left unpolished and painted black. Further, a new statistics based positioning (SBP) algorithm has been implemented to address linearity and edge effect artifacts that are inherent with conventional Anger style positioning schemes. To characterize the light response function (LRF) of the detector, data were collected on a coarse grid using a highly collimated coincidence setup. The LRF was then estimated using cubic spline interpolation. Detector performance has been evaluated for both SBP and Anger based decoding using measured data and Monte Carlo simulations. Results: Using the SBP scheme, edge artifacts were successfully handled. Simulation results show that the useful field of view (UFOV) was extended to ∼22×22 mm 2 with an average point spread function of ∼0.5 mm full width of half maximum (FWHM PSF). For the same detector with Anger decoding the UFOV of the detector was ∼16×16 mm 2 with an average FWHM PSP of ∼0.9 mm. Experimental results yielded similar differences between FOV and resolution performance. FWHM PSF for the SBP and Anger based method was 1.4 and 2.0 mm, uncorrected for source size, with a 1 mm diameter point source, respectively. Conclusion: A continuous detector module with an average FWHM PSF approaching one millimeter has been built and tested. Furthermore, the results demonstrate that our SBP scheme yields improved performance over traditional Anger techniques for our cMiCE detector.