Data Corrections

Objective. Scattered events add bias in the reconstructed positron emission tomography (PET) images. Our objective is the accurate estimation of the scatter distribution, required for an effective scatter correction. 

Approach. In this paper, we propose a practical energy-based (EB) scatter estimation method that uses the marked difference between the energy distribution of the non-scattered and scattered events in the presence of randoms. In contrast to previous EB methods, we model the unscattered events using data obtained from measured point sources. 

Main results. We demonstrate feasibility using Monte Carlo simulated as well as experimental data acquired on the long axial field-of-view (FOV) PennPET EXPLORER scanner. Simulations show that the EB scatter estimated sinograms, for all phantoms, are in excellent agreement with the ground truth scatter distribution, known from the simulated data. Using the standard NEMA image quality (IQ) phantom we find that both the EB and single scatter simulation (SSS) provide good contrast recovery values. However, the EB correction gives better lung residuals.

Significance. Application of the EB method on measured data showed, that the proposed method can be successfully translated to real-world PET scanners. When applied to a 20 cm diameter ×20 cm long cylindrical phantom the EB and SSS algorithms demonstrated very similar performance. However, on a larger 35 cm × 30 cm long cylinder the EB can better account for increased multiple scattering and out-of-FOV activity, providing more uniform images with 12%-36% reduced background variability. In typical PET ring sizes, the EB estimation can be performed in a matter of a few seconds compared to the several minutes needed for SSS, leading to efficiency advantages over the SSS implementation. as well.

Previously, we proposed to use a coincidence collimator to achieve fractional-crystal resolution in positron emission tomography (PET) imaging. We have designed and fabricated a collimator prototype for a small-animal PET scanner (A-PET). To compensate for imperfections in the fabricated collimator prototype, collimator normalization, as well as scanner normalization, is required to reconstruct quantitative and artifact-free images. In this paper, we develop a normalization method for the collimator prototype based on the A-PET normalization using a uniform cylinder phantom. We performed data acquisition without the collimator for scanner normalization first, and then with the collimator from eight different rotation views for collimator normalization. After a reconstruction without correction, we extracted the cylinder parameters from which we generated expected emission sinograms. Single scatter simulation was used to generate the scattered sinograms. We used the least-squares method to generate the normalization coefficient for each line of response (LOR) based on measured, expected, and scattered sinograms. The scanner and collimator normalization coefficients were factorized by performing two normalizations separately. The normalization methods were also verified using experimental data acquired from A-PET with and without the collimator. In summary, we developed a model-based collimator normalization that can significantly reduce variance and produce collimator normalization with adequate statistical quality within feasible scan time.

Purpose: Triple coincidences in positron emission tomography (PET) are events in which three γ‐rays are detected simultaneously. These events, though potentially useful for enhancing the sensitivity of PET scanners, are discarded or processed without special consideration in current systems, because there is not a clear criterion for assigning them to a unique line‐of‐response (LOR). Methods proposed for recovering such events usually rely on the use of highly specialized detection systems, hampering general adoption, and/or are based on Compton‐scatter kinematics and, consequently, are limited in accuracy by the energy resolution of standard PET detectors. In this work, the authors propose a simple and general solution for recovering triple coincidences, which does not require specialized detectors or additional energy resolution requirements.

Methods: To recover triple coincidences, the authors’ method distributes such events among their possible LORs using the relative proportions of double coincidences in these LORs. The authors show analytically that this assignment scheme represents the maximum‐likelihood solution for the triple‐coincidence distribution problem. The PET component of a preclinical PET/CT scanner was adapted to enable the acquisition and processing of triple coincidences. Since the efficiencies for detecting double and triple events were found to be different throughout the scanner field‐of‐view, a normalization procedure specific for triple coincidences was also developed. The effect of including triple coincidences using their method was compared against the cases of equally weighting the triples among their possible LORs and discarding all the triple events. The authors used as figures of merit for this comparison sensitivity, noise‐equivalent count (NEC) rates and image quality calculated as described in the NEMA NU‐4 protocol for the assessment of preclinical PET scanners.

Results: The addition of triple‐coincidence events with the authors’ method increased peak NEC rates of the scanner by 26.6% and 32% for mouse‐ and rat‐sized objects, respectively. This increase in NEC‐rate performance was also reflected in the image‐quality metrics. Images reconstructed using double and triple coincidences recovered using their method had better signal‐to‐noise ratio than those obtained using only double coincidences, while preserving spatial resolution and contrast. Distribution of triple coincidences using an equal‐weighting scheme increased apparent system sensitivity but degraded image quality. The performance boost provided by the inclusion of triple coincidences using their method allowed to reduce the acquisition time of standard imaging procedures by up to ∼25%.

Conclusions: Recovering triple coincidences with the proposed method can effectively increase the sensitivity of current clinical and preclinical PET systems without compromising other parameters like spatial resolution or contrast.

In positron emission tomography (PET) imaging, attenuation correction with accurate attenuation estimation is crucial for quantitative patient studies. Recent research showed that the attenuation sinogram can be determined up to a scaling constant utilizing the time-of-flight information. The TOFPET data can be naturally and efficiently stored in a histo-image without information loss, and the radioactive tracer distribution can be efficiently reconstructed using the DIRECT approaches. In this paper, we explore transmission-less attenuation estimation from TOF-PET histo-images. We first present the TOF-PET histo-image formation and the consistency equations in the histo-image parameterization, then we derive a least-squares solution for estimating the directional derivatives of the attenuation factors from the measured emission histo-images. Finally, we present a fast solver to estimate the attenuation factors from their directional derivatives using the discrete sine transform and fast Fourier transform while considering the boundary conditions. We find that the attenuation histo-images can be uniquely determined from the TOF-PET histo-images by considering boundary conditions. Since the estimate of the attenuation directional derivatives can be inaccurate for LORs tangent to the patient boundary, external sources, e.g. a ring or annulus source, might be needed to give an accurate estimate of the attenuation gradient for such LORs. The attenuation estimation from TOF-PET emission histo-images is demonstrated using simulated 2D TOF-PET data.

In this paper, we present a timing calibration technique for time-of-flight positron emission tomography (TOF PET) that eliminates the need for a specialized data acquisition. By eliminating the acquisition, the process becomes fully automated, and can be performed with any clinical data set and whenever computing resources are available. It also can be applied retroactively to datasets for which a TOF offset calibration is missing or suboptimal. Since the method can use an arbitrary data set to perform a calibration prior to a TOF reconstruction, possibly of the same data set, one also can view this as reconstruction from uncalibrated data. We present a performance comparison with existing calibration techniques.

It has been shown that I-124 PET imaging can be used for accurate dose estimation in radio-immunotherapy techniques. However, I-124 is not a pure positron emitter, leading to two types of coincidence events not typically encountered: increased random coincidences due to non-annihilation cascade photons, and true coincidences between an annihilation photon and primarily a coincident 602 keV cascade gamma (true coincidence gamma-ray background). The increased random coincidences are accurately estimated by the delayed window technique. Here we evaluate the radial and time distributions of the true coincidence gamma-ray background in order to correct and accurately estimate lesion uptake for I-124 imaging in a time-of-flight (TOF) PET scanner. We performed measurements using a line source of activity placed in air and a water-filled cylinder, using F-18 and I-124 radio-isotopes. Our results show that the true coincidence gamma-ray backgrounds in I-124 have a uniform radial distribution, while the time distribution is similar to the scattered annihilation coincidences. As a result, we implemented a TOF-extended single scatter simulation algorithm with a uniform radial offset in the tail-fitting procedure for accurate correction of TOF data in I-124 imaging. Imaging results show that the contrast recovery for large spheres in a uniform activity background is similar in F-18 and I-124 imaging. There is some degradation in contrast recovery for small spheres in I-124, which is explained by the increased positron range, and reduced spatial resolution, of I-124 compared to F-18. Our results show that it is possible to perform accurate TOF based corrections for I-124 imaging.

In this paper we propose a comprehensive energy-based scatter correction approach for positron emission tomography (PET). We take advantage of the marked difference between the energy spectra of the unscattered and scattered photons, and use the detailed energy information that comes with the list-mode data for the estimation of the scattered events distribution in the data space. Also, inside the maximum-likelihood expectation maximization (ML-EM) image reconstruction algorithm, we introduce energy-dependent factors that individualize the correction terms for each event, given its position and energy information. The central piece of our approach is the two-dimensional detector energy response model represented as a linear combination of four components, each one representing a particular state a PET event can be found in: both photons unscattered, the second scattered while the first not, the first photon scattered while the second not and both photons scattered. For a set of events collected in the vicinity of a point in the projection space, the coefficient of each component is determined by applying a statistical estimator. As a result we obtain the number of scattered events that are in the given set. The model also gives us the variation of scatter fraction with the photon pair energies for that particular position in the data space. A simulation study that demonstrates the proposed methods is presented.

We describe a new implementation of a single scatter simulation (SSS) algorithm for the prediction and correction of scatter in 3D PET. In this implementation, out of field of view (FoV) scatter and activity, side shields and oblique tilts are explicitly modelled. Comparison of SSS predictions with Monte Carlo simulations and experimental data from uniform, line and cold-bar phantoms showed that the code is accurate for uniform as well as asymmetric objects and can model different energy resolution crystals and low level discriminator (LLD) settings. Absolute quantitation studies show that for most applications, the code provides a better scatter estimate than the tail-fitting scatter correction method currently in use at our institution. Several parameters such as the density of scatter points, the number of scatter distribution sampling points and the axial extent of the FoV were optimized to minimize execution time, with particular emphasis on patient studies. Development and optimization were carried out in the case of GSObased scanners, which enjoy relatively good energy resolution. SSS estimates for scanners with lower energy resolution may result in different agreement, especially because of a higher fraction of multiple scatter events. The algorithm was applied to a brain phantom as well as to clinical whole-body studies. It proved robust in the case of large patients, where the scatter fraction increases. The execution time, inclusive of interpolation, is typically under 5 min for a whole-body study (axial FoV: 81 cm) of a 100 kg patient.

The feasibility of a new method of attenuation correction in PET has been investigated, using a single-photon emitter for the transmission scan. The transmission scan is predicted to be more than a factor of ten faster with the singles method than the standard coincidence method, for comparable statistics. Thus, a transmission scan can be completed in 1-2 min, rather than 10-20 min, as is common practice with the coincidence method. In addition, a potential advantage of using the single-photon source ¹³⁷Cs, which has an energy of 662 keV, is that postinjection transmission studies can be performed using energy discrimination to separate the transmission from the emission data at 511 keV. In order to compensate for the energy difference of the attenuation coefficients at 662 keV compared to 511 keV, the transmission images are segmented into two compartments, tissue and lung, and known values (for 511 keV) of attenuation are inserted into these compartments. This technique also compensates for the higher amount of scatter present with the singles method, since it is not possible to use a position gate (based on collinearity of the source and two detector positions) as is commonly done with a positron-emitting source. The authors have demonstrated, with experimental phantom studies, that the singles transmission method combined with segmentation gives results equivalent both qualitatively and quantitatively to the coincidence method, but requires significantly less time.

Quantitative, low noise, measured attenuation correction has been established for the PENN PET 240H Volume Imaging Camera. This is achieved, without septa, using a narrow energy (450-570 keV) and sinogram position (2 cm wide mask) gate to minimize scatter contamination. Twelve minute transmission acquisitions with a 0.5 mCi rod source are adequate for this purpose. Post injection transmission scans (with emission activity in the FOV) suffer from emission contamination simulating transmitted gamma ray flux. This emission contamination may be measured by performing a transmission acquisition with normal transmission energy and position gating but without a transmission source. This contamination is then subtracted from the measured post injection transmission scan. Emission activity within the FOV adds to detector deadtime, whereas only a small fraction of events are accepted into the transmission position gate, resulting in a net loss of scan statistics when compared to pre-injection transmission scanning. Removal of emission contamination and compensation for this excess deadtime results in corrected attenuation coefficients close to pre-injection values. For residual activity levels typical of FDG whole-body cancer and cardiac studies the post injection measurements are within 4% of pre-injection values.<>

The acquisition of positron-emission-tomography (PET) transmission information after tracer injection using ring and rotating pin transmission sources is discussed. A combined transmission/emission scan was acquired, followed by an emission scan used to substract the emission counts from the transmission/emission data. The ratio of emission count rate for brain scans to transmission count rate is 50-100% for a 5-mCi ring source and less than 5% for a 5-mCi pin source. Windowing of the sinogram, which rejects most random and scattered coincidences, also eliminates most emission counts. The magnitude and effects of residual random and scattered coincidences as well as increases in variability from transmission/emission scans were studied. The results of combined transmission/emission scans for a high-contrast emission source distribution using ring and pin sources are also described.<>

A method to correct for the spatial distortions of gamma cameras has been developed. The method consists of two parts: measuring spatial distortions and repositioning events during accumulation. Distortions are measured using a pattern consisting of parallel slits on 15-mm centers with slit-pattern images obtained in two orthogonal orientations. Slit locations are used to determine X and Y displacements. In repositioning camera events, X and Y event coordinates are digitized and correction displacements added. The procedure is implemented in hardware that repositions each event in real time without introducing additional dead time. Distortion removal offers considerable advantage over other uniformity improvement schemes, since it correctly compensates for the major cause of non-uniformity, spatial distortion.The method may be used for quantitative studies, because it does not change the number of detected events.