Steven G. Ross

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.

Quantitative comparison of OSEM and penalized likelihood image reconstruction using relative difference penalties for clinical PET.

Ordered subset expectation maximization (OSEM) is the most widely used algorithm for clinical PET image reconstruction. OSEM is usually stopped early and post-filtered to control image noise and does not necessarily achieve optimal quantitation accuracy. As an alternative to OSEM, we have recently implemented a penalized likelihood (PL) image reconstruction algorithm for clinical PET using the relative difference penalty with the aim of improving quantitation accuracy without compromising visual image quality. Preliminary clinical studies have demonstrated visual image quality including lesion conspicuity in images reconstructed by the PL algorithm is better than or at least as good as that in OSEM images. In this paper we evaluate lesion quantitation accuracy of the PL algorithm with the relative difference penalty compared to OSEM by using various data sets including phantom data acquired with an anthropomorphic torso phantom, an extended oval phantom and the NEMA image quality phantom; clinical data; and hybrid clinical data generated by adding simulated lesion data to clinical data. We focus on mean standardized uptake values and compare them for PL and OSEM using both time-of-flight (TOF) and non-TOF data. The results demonstrate improvements of PL in lesion quantitation accuracy compared to OSEM with a particular improvement in cold background regions such as lungs.

Compartmental modeling of technetium-99m-labeled teboroxime with dynamic single-photon emission computed tomography: comparison with static thallium-201 in a canine model.

Di Bella EVR, Ross SG, Kadrmas DJ, et al. Compartmental modeling of technetium-99m–labeled teboroxime with dynamic single-photon emission computed tomography: Comparison with static thallium-201 in a canine model. Invest Radiol 2001;36:178–185. rationale and objectives. A compartmental modeling approach to deriving kinetic parameters from a time series of single-photon emission computed tomography (SPECT) images of technetium-99m–labeled (99mTc-) teboroxime may have value for semiquantitative assessment of myocardial perfusion. This study investigated the value of the kinetic parameters derived from a two-compartment model of 99mTc-teboroxime for measuring myocardial perfusion and compared it with static thallium-201 (201Tl) uptake and microsphere-measured blood flow in dogs. methods.Experiments were successfully conducted in 9 of 11 open-chest dogs. During adenosine stress, a single complete set of projections of 201Tl uptake was acquired. 99mTc-teboroxime was then injected during adenosine stress, and a complete set of projections was acquired every 5.7 seconds for 17 minutes. Resting studies were performed on 4 of the animals. All of the projection sets were reconstructed with an iterative algorithm and incorporated corrections for attenuation and the geometric response of the collimators. Regional kinetic parameters (washin and washout) were determined semiautomatically from the time series of reconstructed 99mTc-teboroxime images and registered with microsphere data. Regional washin estimates were compared with 201Tl intensities and myocardial blood flows determined from microspheres. results.Optimally scaled 99mTc-teboroxime washin parameters and 201Tl uptakes were correlated with microsphere-determined blood flows (r = 0.91, y = 0. 99 x + 0.01, and r = 0.92, y = 0.88 x + 0.28, respectively). In six of the studies, the left anterior descending coronary artery was occluded, and stress occluded-to-normal (O/N) ratios were calculated. The O/N ratios were 0.32 ± 0.17 as determined from microspheres injected with 201Tl and 0.38 ± 0.29 from microspheres injected with 99mTc-teboroxime (P = NS). The O/N ratios were 0.48 ± 0.16 for static 201Tl uptake and 0.27 ± 0.21 for 99mTc-teboroxime washin (P < 0.05). conclusions.Both 201Tl uptake and 99mTc-teboroxime kinetic parameters were well correlated with flow. The 99mTc-teboroxime washin parameters offer semiquantitative flow values and provide greater defect contrast than can be obtained with 201Tl uptake values.

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.

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.

Out-of-field scatter estimation in 3D whole body PET

Many implementations of model based scatter correction (MBSC) are based on the single scatter simulation (SSS) formulation within the scan field-of-view (FOV). A fully 3D approach that models both the axial and trans-axial scatter components can accurately model scatter from hot regions in neighboring slices and outside the scan FOV resulting in greater quantitative accuracy. Herein we discuss how to incorporate the estimation of out-of-field scatter in fully 3D MBSC.

Power laws for image quality measures in PET penalized-likelihood image reconstruction

Most image reconstruction methods have parameters for users to determine: for example, an iteration number and post-reconstruction filter parameters in OSEM, or a regularization parameter in penalized-likelihood (PL). To optimize such reconstruction parameters, one needs to quantitatively understand the relationship among those parameters and image quality. However, image quality is a function of not only the reconstruction parameters but also patient, scanner and imaging protocol. A major advantage of PL over OSEM is the availability of a computationally efficient algebraic procedure to predict resolution and noise properties as a function of the regularization parameter for a given sinogram data set while taking into account the dependence on patient, scanner and protocol. But the procedure, which is based on discrete-space matrix and vector operations, despite its usefulness, lacks intuitive insights such as can be obtained from studying continuous-space Radon transforms. Here, by continuous-space analysis of PL with quadratic (or Gaussian) penalties, we derive approximate yet insightful closed-form expressions for functional relationships, which turn out to be power laws, among the regularization parameter and such image quality measures as resolution, variance and spatial correlation. The expressions we derive provide intuitive insights into how a regularization parameter affects the image quality measures. As a by-product, we develop an understanding of why the ensemble voxel variance in PL is a function of the regularization parameter only and is, somewhat surprisingly, independent of other factors including patient size, scan time and dose.

A phantom study of regularized image reconstruction in PET

Image quality was measured for varied tuning parameters of four penalized likelihood potential functions with reconstructed PET data of multiple hot spheres in a warm background. Statistical image reconstruction with potential functions that penalize differences in neighboring image voxels can produce a smoother image, but large differences that occur at physical boundaries should not be penalized and allowed to form. Over-smoothing PET images with small lesions is especially problematic because it can completely smooth a lesions intensities into the background. Fourteen 1.0-cm spheres with a 6:1 radioactivity concentration relative to the warm background were positioned throughout a 40-cm long phantom with a 36×21-cm oval cross section. By varying the tuning parameters, multiple image sets were reconstructed with modified block sequential regularized expectation maximization statistical reconstruction algorithm using 4 potential functions: quadratic, generalized Gaussian, logCosh, and Huber. Regions of interest were positioned on the images, and the image quality was measured as contrast recovery, background variability, and signal-to-noise ratio across the ROIs. This phantom study was used to further narrow the choice of potential functions and parameter values to either improve the image quality of small lesions or avoid deteriorating them at the cost of optimizing reconstruction parameters for other image features. Neither the quadratic or logCosh potentials performed well for small lesion SNR because they either over-smoothed the lesions or under-smoothed the background, respectively. Varying the parameter values for the Huber potential had a proportional effect on the background variability and the sphere signal such that SNR was relatively fixed. Generalized Gaussian simultaneously decreased background variability and increased small lesion contrast recovery that produced SNRs as much as two-times higher than the other potential functions.

Improving lesion detectability in PET imaging with a penalized likelihood reconstruction algorithm

Ordered Subset Expectation Maximization (OSEM) is currently the most widely used image reconstruction algorithm for clinical PET. However, OSEM does not necessarily provide optimal image quality, and a number of alternative algorithms have been explored. We have recently shown that a penalized likelihood image reconstruction algorithm using the relative difference penalty, block sequential regularized expectation maximization (BSREM), achieves more accurate lesion quantitation than OSEM, and importantly, maintains acceptable visual image quality in clinical wholebody PET. The goal of this work was to evaluate lesion detectability with BSREM versus OSEM. We performed a twoalternative forced choice study using 81 patient datasets with lesions of varying contrast inserted into the liver and lung. At matched imaging noise, BSREM and OSEM showed equivalent detectability in the lungs, and BSREM outperformed OSEM in the liver. These results suggest that BSREM provides not only improved quantitation and clinically acceptable visual image quality as previously shown but also improved lesion detectability compared to OSEM. We then modeled this detectability study, applying both nonprewhitening (NPW) and channelized Hotelling (CHO) model observers to the reconstructed images. The CHO model observer showed good agreement with the human observers, suggesting that we can apply this model to future studies with varying simulation and reconstruction parameters.

Evaluation of lesion detectability in positron emission tomography when using a convergent penalized likelihood image reconstruction method

Abstract. We have previously developed a convergent penalized likelihood (PL) image reconstruction algorithm using the relative difference prior (RDP) and showed that it achieves more accurate lesion quantitation compared to ordered subsets expectation maximization (OSEM). We evaluated the detectability of low-contrast liver and lung lesions using the PL-RDP algorithm compared to OSEM. We performed a two-alternative forced choice study using a channelized Hotelling observer model that was previously validated against human observers. Lesion detectability showed a stronger dependence on lesion size for PL-RDP than OSEM. Lesion detectability was improved using time-of-flight (TOF) reconstruction, with greater benefit for the liver compared to the lung and with increasing benefit for decreasing lesion size and contrast. PL detectability was statistically significantly higher than OSEM for 20 mm liver lesions when contrast was ≥0.5 (p<0.05), and TOF PL detectability was statistically significantly higher than TOF OSEM for 15 and 20 mm liver lesions with contrast ≥0.5 and ≥0.25, respectively. For all other cases, there was no statistically significant difference between PL and OSEM (p>0.05). For the range of studied lesion properties, lesion detectability using PL-RDP was equivalent or improved compared to using OSEM.