William C. J. Hunter

Maximum-Likelihood Methods for Processing Signals From Gamma-Ray Detectors

In any gamma-ray detector, each event produces electrical signals on one or more circuit elements. From these signals, we may wish to determine the presence of an interaction; whether multiple interactions occurred; the spatial coordinates in two or three dimensions of at least the primary interaction; or the total energy deposited in that interaction. We may also want to compute listmode probabilities for tomographic reconstruction. Maximum-likelihood methods provide a rigorous and in some senses optimal approach to extracting this information, and the associated Fisher information matrix provides a way of quantifying and optimizing the information conveyed by the detector. This paper will review the principles of likelihood methods as applied to gamma-ray detectors and illustrate their power with recent results from the Center for Gamma-ray Imaging.

SemiSPECT: A small-animal single-photon emission computed tomography (SPECT) imager based on eight cadmium zinc telluride (CZT) detector arrays

The first full single-photon emission computed tomography (SPECT) imager to exploit eight compact high-intrinsic-resolution cadmium zinc telluride (CZT) detectors, called SemiSPECT, has been completed. Each detector consists of a CZT crystal and a customized application-specific integrated circuit (ASIC). The CZT crystal is a 2.7 cm x 2.7 cm x -0.2 cm slab with a continuous top electrode and a bottom electrode patterned into a 64 x 64 pixel array by photolithography. The ASIC is attached to the bottom of the CZT crystal by indium-bump bonding. A bias voltage of -180 V is applied to the continuous electrode. The eight detectors are arranged in an octagonal lead-shielded ring. Each pinhole in the eight-pinhole aperture placed at the center of the ring is matched to each individual detector array. An object is imaged onto each detector through a pinhole, and each detector is operated independently with list-mode acquisition. The imaging subject can be rotated about a vertical axis to obtain additional angular projections. The performance of SemiSPECT was characterized using 99mTc. When a 0.5 mm diameter pinhole is used, the spatial resolution on each axis is about 1.4 mm as estimated by the Fourier crosstalk matrix, which provides an algorithm-independent average resolution over the field of view. The energy resolution achieved by summing neighboring pixel signals in a 3 x 3 window is about 10% full-width-at-half-maximum of the photopeak. The overall system sensitivity is about 0.5 x 10(-4) with the energy window of +/-10% from the photopeak. Line-phantom images are presented to visualize the spatial resolution provided by SemiSPECT, and images of bone, myocardium, and human tumor xenografts in mice demonstrate the feasibility of preclinical small-animal studies with SemiSPECT.

Calibration Method for ML Estimation of 3D Interaction Position in a Thick Gamma-Ray Detector

High-energy (> 100 keV) photon detectors are often made thick relative to their lateral resolution in order to improve their photon-detection efficiency. To avoid issues of parallax and increased signal variance that result from random interaction depth, we must determine the 3D interaction position in the imaging detector. With this goal in mind, we examine a method of calibrating response statistics of a thick-detector gamma camera to produce a maximum-likelihood estimate of 3D interaction position. We parameterize the mean detector response as a function of 3D position, and we estimate these parameters by maximizing their likelihood given prior knowledge of the pathlength distribution and a complete list of camera signals for an ensemble of gamma-ray interactions. Furthermore, we describe an iterative method for removing multiple-interaction events from our calibration data and for refining our calibration of the mean detector response to single interactions. We demonstrate this calibration method with simulated gamma-camera data. We then show that the resulting calibration is accurate and can be used to produce unbiased estimates of 3D interaction position.

SemiSPECT: a small-animal imaging system based on eight CdZnTe pixel detectors

We have constructed a SPECT system for small animals that utilizes eight CdZnTe pixel detectors. The eight detectors are arranged in a single octagonal ring, where each views the object to be imaged through a single pinhole. Additional projections are obtained via rotation of the animal. Each CdZnTe detector is approximately 2 mm in thickness and is patterned on one surface into a 64/spl times/64 array of pixels with 380 micron pitch. We have designed an electronic readout system capable of collecting data front the eight detectors in listmode. In this scheme each event entry for a gamma-ray hit includes the pulse height of the pixel with the largest signal and the pulse height for each of its eight nearest neighbors. We present details of the overall design, the electronics, and system performance.

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.

Effective count rates for PET scanners with reduced and extended axial field of view

We investigated the relationship between noise equivalent count (NEC) and axial field of view (AFOV) for PET scanners with AFOVs ranging from one-half to twice those of current clinical scanners. PET scanners with longer or shorter AFOVs could fulfill different clinical needs depending on exam volumes and site economics. Using previously validated Monte Carlo simulations, we modeled true, scattered and random coincidence counting rates for a PET ring diameter of 88 cm with 2, 4, 6, and 8 rings of detector blocks (AFOV 7.8, 15.5, 23.3, and 31.0 cm). Fully 3D acquisition mode was compared to full collimation (2D) and partial collimation (2.5D) modes. Counting rates were estimated for a 200 cm long version of the 20 cm diameter NEMA count-rate phantom and for an anthropomorphic object based on a patient scan. We estimated the live-time characteristics of the scanner from measured count-rate data and applied that estimate to the simulated results to obtain NEC as a function of object activity. We found NEC increased as a quadratic function of AFOV for 3D mode, and linearly in 2D mode. Partial collimation provided the highest overall NEC on the 2-block system and fully 3D mode provided the highest NEC on the 8-block system for clinically relevant activities. On the 4-, and 6-block systems 3D mode NEC was highest up to ∼300 MBq in the anthropomorphic phantom, above which 3D NEC dropped rapidly, and 2.5D NEC was highest. Projected total scan time to achieve NEC-density that matches current clinical practice in a typical oncology exam averaged 9, 15, 24, and 61 min for the 8-, 6-, 4-, and 2-block ring systems, when using optimal collimation. Increasing the AFOV should provide a greater than proportional increase in NEC, potentially benefiting patient throughput-to-cost ratio. Conversely, by using appropriate collimation, a two-ring (7.8 cm AFOV) system could acquire whole-body scans achieving NEC-density levels comparable to current standards within long, but feasible, scan times.

Maximum-likelihood estimation of 3D event position in monolithic scintillation crystals: Experimental results

We present a simple 3D event position-estimation method using raw list-mode acquisition and maximum-likelihood estimation in a modular gamma camera with a thick (25 mm) monolithic scintillation crystal. This method involves measuring 2D calibration scans with a well-collimated 511 keV source and fitting each point to a simple depth-dependent light distribution model. Preliminary results show that angled collimated beams appear properly reconstructed.

Light-sharing interface for dMiCE detectors using sub-surface laser engraving

We have previously reported on dMiCE, a method of resolving depth or interaction (DOI) in a pair of discrete crystals by encoding light sharing properties as a function of depth in the interface of a crystal-element pair. A challenge for this method is the cost and repeatability of interface treatment for each crystal pair. In this work, we report our preliminary results on using sub-surface laser engraving (SSLE) as a means of forming this depth-dependent interface in a dMiCE detector. A surplus first-generation SSLE system was used to create a partially reflective layer 100-microns thick at the boundary between two halves of a 1.4-by-2.9-by- 20 mm3 LYSO crystal. The boundary of these paired crystal elements was positioned between two 3-mm wide Silicon photomultiplier arrays. The responses of these two photodetectors were acquired for an ensemble of 511-keV photons collimated to interact at a fixed depth in just one crystal element. Interaction position was then varied to measure detector response as a function of depth, which was then used to maximum-likelihood positions. Despite use of sub-optimal SSLE processing we found an average DOI resolution of 3.4 mm for front-sided readout and 3.9 mm for back-sided readout while obtaining energy resolutions on the order of 10%. We expect DOI resolution can be improved significantly by optimizing the SSLE process and pattern.

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 50X50X15-mm3 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 49.2X49.2X15 mm3 LYSO crystal readout by a 12X12 array of 3.8X3.8-mm2 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.

Design of a second generation firewire based data acquisition system for small animal PET scanners

The University of Washington developed a Firewire based data acquisition system for the MiCES small animal PET scanner. Development work has continued on new imaging scanners that require more data channels and need to be able to operate within a MRI imaging system. To support these scanners, we have designed a new version of our data acquisition system that leverages the capabilities of modern field programmable gate arrays (FPGA). The new design preserves the basic approach of the original system, but puts almost all functions into the FPGA, including the Firewire elements, the embedded processor, and pulse timing and pulse integration. The design has been extended to support implementation of the position estimation and DOI algorithms developed for the cMiCE detector module. The design is centered around an acquisition node board (ANB) that includes 65 ADC channels, Firewire 1394b support, the FPGA, a serial command bus and signal lines to support a rough coincidence window implementation to reject singles events from being sent on the Firewire bus. Adapter boards convert detector signals into differential paired signals to connect to the ANB.