C.E. Ordonez

Simulation of imaging with sodium iodide crystals and position-sensitive photomultiplier tubes

The imaging characteristics of miniature gamma cameras that consist of a single sodium iodide (NaI(Tl)) crystal coupled to a position-sensitive photomultiplier tube (PSPMT) have been studied via Monte Carlo simulations. Images obtained with such cameras with the use of conventional position calculations exhibit considerable distortions, particularly compression. This study demonstrates that the distortions result primarily from nonuniform sensitivities of PSPMTs and secondarily from nonlinear responses of PSPMTs, light-reflection properties resulting from the treatments of crystals, and light-refractive properties of glass interfaces between crystals and photocathodes. Simulation results are compared to images obtained with a prototype miniature gamma camera. >

A Single-tube Miniature Gamma Camera

A Single-Tube Miniature Gamma Camera NJ Yasillo, RA Mintzer, JN Aarsvold, KL Matthews, SJ Heimsath, CE Ordonez, X Pan, C Wu, TA Block, RN Beck, C-T Chen, and M Cooper Franklin McLean Memorial Research Institute, The University of Chicago 5841 S. Maryland Ave., MC-1037, Chicago, IL 60637 In certain medical gamma imaging applications, conventional cameras are too large for practical use. To address these situations, we have constructed a clinically usable miniature gamma camera for photon energies up to 160 keV. The camera has outer dimensions of 92 mm x 92 mm x 190 mm and weighs 5 kg. Included in that mass is a collimator, an internal high-voltage power supply, and all shielding. The camera also has a position-sensitive photomultiplier tube (PSPMT) coupled to an 8-mm thick NaI(Tl) crystal; this crystal/tube combination provides signals to internal processing circuits. External electronics and analog-to-digital conversion circuits are connected to a Macintosh Quadra computer where additional processing, storage, and display of the signals takes place. Because the PSPMT has non-uniform energy response that results in geometric distortion if conventional position-arithmetic calculations are used, we have implemented a maximumlikelihood position-estimation calculation that produces undistorted images. The present version of the camera has a usable field of view of 48 mm x 48 mm and an intrinsic spatial resolution of 2.4 to 3.8 mm full width at half maximum.

Simulation of light output from narrow sodium iodide detectors

The use of narrow scintillators in imaging devices raises the question of whether there is enough light output that can yield reasonable energy and spatial resolutions. Compared to scintillation within large-area detectors (such as those used in conventional gamma cameras), scintillation photons within narrow detectors are expected to undergo more reflections because of the proximity of the detector surfaces. In this study, we use simulation methods to estimate the light output from long, narrow sodium iodide crystals, and to investigate the effects of detector geometry and detector surface reflection properties on the fraction of scintillation photons that are able to leave the crystal through the exit window (on one of the long, narrow sides). Our simulations show that the light output from a 3.5-mm wide by 10-mm high by 300-mm long detector can result in reasonable energy resolutions. Our simulations also suggest that, in conjunction with the use of external reflectors, a crystal that has its sides polished to a smooth finish results in better light output than one with sides grounded to a rough finish.

Implementations of Maximum-Likelihood Position Estimation in a Four-PMT Scintillation Detector

Maximum-likelihood (ML) position estimation in small scintillation detectors often involves the use of a look-up table (LUT) to map event characterization vectors to the associated position estimates. As the number of possible characterization vectors determines the size of the LUT, the number of these vectors needs to be manageable. This implies that a critical component of an implementation of ML position estimation is the mapping of detector output signals to characterization vectors. The use of different photomultiplier tube (PMT) output mappings in ML estimation in a small camera with four round PMTs and a single 5 x 100 x 100 mm NaI(T1) crystal was investigated. The employed mappings of the four detector signals resulted in 20 (5 bits/PMT), 22 (8 bits each for Anger x and y; 6 bits for the sum signal), 24 (6 bits/PMT), and 28 (7 bits/PMT) bit event characterizations. Using present implementations of ML estimation, significant improvement in image quality results if a 24-bit characterization is used rather than 20 or 22. Improvement in image quality is not as marked when 28-bit characterization is used instead of 24, but measurable improvement is obtained.

The interaction of collimator lattice periodicity and detector pixelation

Collimators, which are just periodic arrays of holes in lead, are used on gamma cameras in nuclear medicine to create images. Generally, the collimator hole pattern is not visible in clinical images because the holes are separated by distances smaller than the intrinsic resolution of the gamma camera. However, new (CZT) solid-state detectors are characterized by a regular grid of detector pixels. The interaction between the collimator-hole lattice and the detector grid almost assures that moire patterns will appear in the images unless the two grids are commensurate. Unfortunately, collimators with hole spacings commensurate with the pixel size are far from optimal in nuclear medicine. A mathematical analysis of the imaging process in such systems is provided and used to demonstrate the effects. Two strategies for minimizing the effects are examined: (1) introducing a gap between the collimator and the detector and (2) constructing the collimator with numerous small segments with displaced grid structures. Both strategies have serious drawbacks.

Scatter correction for 3-D PET by convolution of plane-integral projections

The authors have studied the scatter characteristics of three-dimensional (3D) positron emission tomography (PET) in terms of the plane-integral scatter response function (SRF). To obtain the plane-integral SRF and study its properties, the authors carried out Monte Carlo simulations to generate coincidence events of a point source located at different positions in water-filled spheres of various sizes. The plane-integral SRF is obtained by rebinning the detected true and scatter events into two separate sets of plane integrals and then dividing the plane integrals of scatter events by the true-event plane integral of the plane in which the point source is located. For these simulations, the authors assumed a spherical PET scanner. The examination of the SRF shows that the SRF in 3D PET can be modeled not by an exponential as in the case of 2D PET, but by a Gaussian with its peak shifted away from the center of the scatter media. Using this plane-integral SRF, the authors have developed a scatter correction method for 3D PET that first converts an attenuation-corrected 3D PET data set into plane integrals, and then obtains the scatter components in the rebinned plane integrals by convolving the rebinned plane integrals with the SRF, and finally subtracts the scatter components from the rebinned plane integrals to yield the scatter-corrected plane integrals. From the scatter-corrected plane integrals, the authors reconstructed a 3D image using a 3D filtered-backprojection algorithm. To test the method, the authors simulated a cylindrical PET scanner imaging an ellipsoid phantom with a 3-cm cold bar at the center, and reconstructed 3D images of the phantom with and without scatter correction. By comparing the two images, the authors found that this method compensates reasonably well for scatter events. The advantages of the proposed method are that it treats the scatter in 3D PET in a truly 3D manner and that it is computationally efficient.<<ETX>>

Maximum-likelihood calibration of small gamma cameras for 511 keV positron annihilation radiation

The feasibility of employing maximum-likelihood (ML) position estimation in small scintillation cameras for use in FDG coincidence imaging was investigated. A small camera consisting of a Hamamatsu R-2487 position-sensitive photomultiplier tube (PSPMT) coupled to a single 8 mm thick NaI(Tl) crystal was calibrated with a tungsten and lead shielded 511 keV /sup 18/F source. The same calibration method has been previously employed at 140 keV using /sup 99m/Tc. The source was positioned at each location of the image space to determine detector-signal distributions used in look-up table (LUT) generation. Corrected 511 keV point-array and flood images were obtained using the resulting 511 keV calibration LUT. Resolution was 2.0 mm-2.5 mm full-width at half maximum (FWHM). This demonstrates that it may be feasible to use ML estimation to obtain accurate event positioning in similar imaging detectors employing more suitable scintillators.

Characterization and correction for scatter in 3D PET using rebinned plane integrals

The scatter characteristics of three-dimensional (3D) positron emission tomography (PET) in terms of the plane-integral scatter response function (SRF) are studied. To obtain the plane-integral SRF and study its properties, Monte Carlo simulations, were carried out which generated coincidence events from point sources located at different positions in water-filled spheres of various sizes. In each simulation, the plane-integral SRF is obtained by rebinning the detected true and scatter events into two separate sets of plane integrals and then dividing the plane integrals of scatter events by the plane integral of true events of the plane in which the point source is located. A spherical PET scanner was assumed for these simulations. Examination of the SRF shows that the SRF in 3D PET can be modeled not by an exponential function as in the case of 2D PET, but by a Gaussian with its peak shifted away from the primary peak. Using this plane-integral SRF a scatter correction method was developed for 3D PET that first converts an attenuation-corrected 3D PET data set into plane integrals, then obtains the scatter components in the rebinned plane integrals by integral transformation of the rebinned plane integrals with the SRF, and finally subtracts the scatter components from the rebinned plane integrals to yield the scatter-corrected plane integrals, From the scatter-corrected plane integrals, a 3D image was reconstructed by using a 3D filtered-backprojection algorithm. To test the method, a cylindrical PET scanner imaging an ellipsoid phantom with a 3-cm cold bar at the center was simulated, and 3D images of the phantom with and without scatter correction were reconstructed. Comparison of the two images shows that this method compensates reasonably well for scatter events. The advantages of the proposed method are that it treats the scatter in 3D PET in a truly 3D manner and that it is computationally efficient. >

Incorporation of structural CT and MR images in PET image reconstruction

A Bayesian method that incorporates a priori information derived from the spatially-correlated structural images in reconstruction of images acquired in positron emission tomography (PET) has been developed for the improvement of image quality. One source of a priori information that potentially can be very useful is the anatomic information extracted from the x-ray computed tomography (CT) and magnetic resonance (MR) images. For example, anatomic structures outlined on the correlated CT or MR images can be incorporated in the Bayesian method to aid in identifying boundaries in PET images. This new approach can improve the quality of the reconstructed PET images.

FIPI: Fast 3-D PET Reconstruction by Fourier Inversion of Rebinned Plane Integrals

A fast reconstruction algorithm for three-dimensional (3-D) positron emission tomography (PET) has been developed by the use of Fourier inversion of rebinned plane integrals (FIPI). The FIPI algorithm rebins 3-D PET data into plane integrals (3-D Radon transforms) and then reconstructs 3-D images by Fourier inversion of the plane integrals. The algorithm was quantitatively evaluated by the use of simulated as well as measured data, and its results were compared to those of two other algorithms: 2-D filtered-backprojection (FBP) and 3-D reprojection. The results indicate that the three algorithms produce images with good and comparable resolution, but the two 3-D PET algorithms yield images with significantly better statistics than does the 2-D FBP algorithm. The results further show that our FIPI algorithm is five times faster than the widely used reprojection algorithm.