Charles W. Stearns

Application and Evaluation of a Measured Spatially Variant System Model for PET Image Reconstruction

Accurate system modeling in tomographic image reconstruction has been shown to reduce the spatial variance of resolution and improve quantitative accuracy. System modeling can be improved through analytic calculations, Monte Carlo simulations, and physical measurements. The purpose of this work is to improve clinical fully-3-D reconstruction without substantially increasing computation time. We present a practical method for measuring the detector blurring component of a whole-body positron emission tomography (PET) system to form an approximate system model for use with fully-3-D reconstruction. We employ Monte Carlo simulations to show that a non-collimated point source is acceptable for modeling the radial blurring present in a PET tomograph and we justify the use of a Na22 point source for collecting these measurements. We measure the system response on a whole-body scanner, simplify it to a 2-D function, and incorporate a parameterized version of this response into a modified fully-3-D OSEM algorithm. Empirical testing of the signal versus noise benefits reveal roughly a 15% improvement in spatial resolution and 10% improvement in contrast at matched image noise levels. Convergence analysis demonstrates improved resolution and contrast versus noise properties can be achieved with the proposed method with similar computation time as the conventional approach. Comparison of the measured spatially variant and invariant reconstruction revealed similar performance with conventional image metrics. Edge artifacts, which are a common artifact of resolution-modeled reconstruction methods, were less apparent in the spatially variant method than in the invariant method. With the proposed and other resolution-modeled reconstruction methods, edge artifacts need to be studied in more detail to determine the optimal tradeoff of resolution/contrast enhancement and edge fidelity.

Validation of GATE Monte Carlo simulations of the GE Advance/Discovery LS PET scanners

The recently developed GATE (GEANT4 application for tomographic emission) Monte Carlo package, designed to simulate positron emission tomography (PET) and single photon emission computed tomography (SPECT) scanners, provides the ability to model and account for the effects of photon noncollinearity, off-axis detector penetration, detector size and response, positron range, photon scatter, and patient motion on the resolution and quality of PET images. The objective of this study is to validate a model within GATE of the General Electric (GE) Advance/Discovery Light Speed (LS) PET scanner. Our three-dimensional PET simulation model of the scanner consists of 12 096 detectors grouped into blocks, which are grouped into modules as per the vendors specifications. The GATE results are compared to experimental data obtained in accordance with the National Electrical Manufactures Association/Society of Nuclear Medicine (NEMA/SNM), NEMA NU 2-1994, and NEMA NU 2-2001 protocols. The respective phantoms are also accurately modeled thus allowing us to simulate the sensitivity, scatter fraction, count rate performance, and spatial resolution. In-house software was developed to produce and analyze sinograms from the simulated data. With our model of the GE Advance/Discovery LS PET scanner, the ratio of the sensitivities with sources radially offset 0 and 10 cm from the scanners main axis are reproduced to within 1% of measurements. Similarly, the simulated scatter fraction for the NEMA NU 2-2001 phantom agrees to within less than 3% of measured values (the measured scatter fractions are 44.8% and 40.9 +/- 1.4% and the simulated scatter fraction is 43.5 +/- 0.3%). The simulated count rate curves were made to match the experimental curves by using deadtimes as fit parameters. This resulted in deadtime values of 625 and 332 ns at the Block and Coincidence levels, respectively. The experimental peak true count rate of 139.0 kcps and the peak activity concentration of 21.5 kBq/cc were matched by the simulated results to within 0.5% and 0.1% respectively. The simulated count rate curves also resulted in a peak NECR of 35.2 kcps at 10.8 kBq/cc compared to 37.6 kcps at 10.0 kBq/cc from averaged experimental values. The spatial resolution of the simulated scanner matched the experimental results to within 0.2 mm.

Properties and Mitigation of Edge Artifacts in PSF-Based PET Reconstruction

PSF (point spread function) based image reconstruction causes an overshoot at sharp intensity transitions (edges) of the object. This edge artifact, or ringing, has not been fully studied. In this work, we analyze the properties of edge artifacts in PSF-based reconstruction in an effort to develop mitigation methods. Our study is based on 1D and 2D simulation experiments. Two approaches are adopted to analyze the artifacts. In the system theory approach, we relate the presence of edge artifacts to the null space and conditioning of the imaging operator. We show that edges cannot be accurately recovered with a practical number of image updates when the imaging matrices are poorly conditioned. In the frequency-domain analysis approach, we calculate the object-specific modulation transfer function (OMTF) of the system, defined as spectrum of the reconstruction divided by spectrum of the object. We observe an amplified frequency band in the OMTF of PSF-based reconstruction and that the band is directly related to the presence of ringing. Further analysis shows the amplified band is linearly related to kernel frequency support (the reciprocal of the reconstruction kernel FWHM), and the relation holds for different objects. Based on these properties, we develop a band-suppression filter to mitigate edge artifacts. We apply the filter to simulation and patient data, and compare its performance with other mitigation methods. Analysis shows the band-suppression filter provides better tradeoff of resolution and ringing suppression than a low-pass filter.

Measured count-rate performance of the Discovery STE PET/CT scanner in 2D, 3D and partial collimation acquisition modes

We measured count rates and scatter fraction on the Discovery STE PET/CT scanner in conventional 2D and 3D acquisition modes, and in a partial collimation mode between 2D and 3D. As part of the evaluation of using partial collimation, we estimated global count rates using a scanner model that combined computer simulations with an empirical live-time function. Our measurements followed the NEMA NU2 count rate and scatter-fraction protocol to obtain true, scattered and random coincidence events, from which noise equivalent count (NEC) rates were calculated. The effect of patient size was considered by using 27 cm and 35 cm diameter phantoms, in addition to the standard 20 cm diameter cylindrical count-rate phantom. Using the scanner model, we evaluated two partial collimation cases: removing half of the septa (2.5D) and removing two-thirds of the septa (2.7D). Based on predictions of the model, a 2.7D collimator was constructed. Count rates and scatter fractions were then measured in 2D, 2.7D and 3D. The scanner model predicted relative NEC variation with activity, as confirmed by measurements. The measured 2.7D NEC was equal or greater than 3D NEC for all activity levels in the 27 cm and 35 cm phantoms. In the 20 cm phantom, 3D NEC was somewhat higher ( approximately 15%) than 2.7D NEC at 100 MBq. For all higher activity concentrations, 2.7D NEC was greater and peaked 26% above the 3D peak NEC. The peak NEC in 2.7D mode occurred at approximately 425 MBq, and was 26-50% greater than the peak 3D NEC, depending on object size. NEC in 2D was considerably lower, except at relatively high activity concentrations. Partial collimation shows promise for improved noise equivalent count rates in clinical imaging without altering other detector parameters.

A fully 3D iterative image reconstruction algorithm incorporating data corrections

In this study, we implemented a fully 3D maximum likelihood ordered subsets expectation maximization (ML-OSEM) reconstruction algorithm with two methods for corrections of randoms, and scatter coincidences: (a) measured data were pre-corrected for randoms and scatter, and (b) corrections were incorporated into the iterative algorithm. In 3D PET acquisitions, the random and scatter coincidences constitute a significant fraction of the measured coincidences. ML-OSEM reconstruction algorithms make assumptions of Poisson distributed data. Pre-corrections for random and scatter coincidences result in deviations from that assumption, potentially leading to increased noise and inconsistent convergence. Incorporating the corrections inside the loop of the iterative reconstruction preserves the Poisson nature of the data. We performed Monte Carlo simulations with different randoms fractions and reconstructed the data with the two methods. We also reconstructed clinical patient images. The two methods were compared quantitatively through contrast and noise measurements. The results indicate that for high levels of randoms, incorporating the corrections inside the iterative loop results in superior image quality.

3D implementation of Scatter Estimation in 3D PET

Successful 3D imaging requires accurate and robust methods for scatter estimation and correction. We developed a computationally efficient fully 3D approach modeling both the axial and trans-axial scatter components. Simulation results showed good agreement with the Monte Carlo scatter and improved image quality (IQ). We tested the proposed algorithm on clinical data with similar IQ improvements.

Fully 3D PET Iterative Reconstruction Using Distance-Driven Projectors and Native Scanner Geometry

Incorporating all data corrections into the system model optimizes image quality in statistical iterative PET image reconstruction. We have previously shown that including attenuation, randoms and scatter in the forward 3D iterative model results in faster convergence and improved image quality for ML-OSEM. This paper extends this work to allow the accurate modeling of crystal efficiency, detector deadtime, and the native block-based detector geometry. In order to model these effects, it is necessary to perform forward and back-projections directly from image space to the projection geometry of the PET scanner, rather than to an idealized, equally spaced projection space. We have modified the distance-driven projectors to accurately model both the uneven spacing of the sinogram due to the ring curvature as well as the gaps resulting from the block structure of the scanner. This results in a reconstruction method, which can incorporate the crystal efficiency and block deadtime effects into the forward system model while maintaining the fast reconstruction times enabled by the distance driven projector design. Results on the GE Discovery STEtrade scanner show improvements in image resolution consistent with removing the interpolative smoothing of the data into the equally spaced projection space.

Impact of PSF modelling on the convergence rate and edge behaviour of EM images in PET

EM reconstructions with point-spread-function (PSF) modelling is performed to increase the spatial resolution in PET images. These images exhibit slower initial convergence compared to reconstructions without PSF modelling. Furthermore, they exhibit more pronounced ringing around the edges of sharp features. We investigate the effect of different objects and PSF modelling on the convergence rate and edge behaviour of the EM algorithm in two stages: (i) at the initial iterations where the updates are large and (ii) at the later iterations where the updates are small. For the initial iterations, we compare the sharpness of the EM updates with and without PSF modelling. We show via simulations that the PSF modelling during the backprojection step causes smoother updates and consequently smoother images in the early stages of the EM algorithm. For the later iterations, we approximate the image as the ML image plus a perturbation term and develop an approximate update equation for the perturbation, which depends on the Hessian (H) of the log-likelihood. Based on this equation and the spectral analysis of H, we demonstrate how edges with ringing are preserved in the later stages of the algorithm and eliminated only for the case of noiseless data reconstruction with an unrealistically high number of iterations. In addition, we provide an intuitive explanation for the creation of the edge artefacts in terms of the PSF modelling during the backprojection step.

Impact of CT attenuation correction method on quantitative respiratory‐correlated (4D) PET/CT imaging

PURPOSE Respiratory-correlated positron emission tomography (PET/CT) 4D PET/CT is used to mitigate errors from respiratory motion; however, the optimal CT attenuation correction (CTAC) method for 4D PET/CT is unknown. The authors performed a phantom study to evaluate the quantitative performance of CTAC methods for 4D PET/CT in the ground truth setting. METHODS A programmable respiratory motion phantom with a custom movable insert designed to emulate a lung lesion and lung tissue was used for this study. The insert was driven by one of five waveforms: two sinusoidal waveforms or three patient-specific respiratory waveforms. 3DPET and 4DPET images of the phantom under motion were acquired and reconstructed with six CTAC methods: helical breath-hold (3DHEL), helical free-breathing (3DMOT), 4D phase-averaged (4DAVG), 4D maximum intensity projection (4DMIP), 4D phase-matched (4DMATCH), and 4D end-exhale (4DEXH) CTAC. Recovery of SUV(max), SUV(mean), SUV(peak), and segmented tumor volume was evaluated as RC(max), RC(mean), RC(peak), and RC(vol), representing percent difference relative to the static ground truth case. Paired Wilcoxon tests and Kruskal-Wallis ANOVA were used to test for significant differences. RESULTS For 4DPET imaging, the maximum intensity projection CTAC produced significantly more accurate recovery coefficients than all other CTAC methods (p < 0.0001 over all metrics). Over all motion waveforms, ratios of 4DMIP CTAC recovery were 0.2 ± 5.4, -1.8 ± 6.5, -3.2 ± 5.0, and 3.0 ± 5.9 for RC(max), RC(peak), RC(mean), and RC(vol). In comparison, recovery coefficients for phase-matched CTAC were -8.4 ± 5.3, -10.5 ± 6.2, -7.6 ± 5.0, and -13.0 ± 7.7 for RC(max), RC(peak), RC(mean), and RC(vol). When testing differences between phases over all CTAC methods and waveforms, end-exhale phases were significantly more accurate (p = 0.005). However, these differences were driven by the patient-specific respiratory waveforms; when testing patient and sinusoidal waveforms separately, patient waveforms were significantly different between phases (p < 0.0001) while the sinusoidal waveforms were not significantly different (p = 0.98). When considering only the subset of 4DMATCH images that corresponded to the end-exhale image phase, 4DEXH, mean and interquartile range were similar to 4DMATCH but variability was considerably reduced. CONCLUSIONS Comparative advantages in accuracy and precision of SUV metrics and segmented volumes were demonstrated with the use of the maximum intensity projection and end-exhale CT attenuation correction. While respiratory phase-matched CTAC should in theory provide optimal corrections, image artifacts and differences in implementation of 4DCT and 4DPET sorting can degrade the benefit of this approach. These results may be useful to guide the implementation, analysis, and development of respiratory-correlated thoracic PET/CT in the radiation oncology and diagnostic settings.

A noise equivalent counts approach to transmission imaging and source design

Noise equivalent counts are a convenient and effective means to assess PET (positron emission tomography) emission image quality. The authors have extended the method to include the effects of transmission imaging on the statistics of attenuation-corrected PET data. The result of the calculations is a noise figure which describes the SNR (signal-to-noise ratio) performance of the elements of the attenuation-corrected emission sinogram. The noise figure demonstrates the trade-off between emission and transmission imaging performance, and can be used to determine optimal partitioning of imaging time between emission and transmission scans. Also, the technique can be used to compare the efficacy of simultaneous transmission/emission imaging techniques and multiple orbiting rod source geometries. Experimental and simulated results from the GE 2048 PET scanner are used to demonstrate the model. In a sample imaging situation in that system geometry (0.2- mu Ci /cm/sup 3/ activity in a 20-cm flood phantom, 3-mCi orbiting rod source(s)), an optimal single rod source protocol achieves a noise figure of 14.2 (arbitrary units); a dual rod source, 11.4; and simultaneous transmission/emission scanning, 10.7.<<ETX>>