M6B1  Image Reconstruction and Data Corrections II

Saturday, Nov. 7  10:30-12:30  Golden Pacific Ballroom

Session Chair:  Jinyi Qi, University of California, Davis, United States; Joyita Dutta, UMass/Harvard/MGH, United States

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(10:30) M6B1-1, FORCE: Fourier Rebinning and Consistency Equations for Time-of-Flight PET

Y. Li, S. Matej, S. D. Metzler

Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA
Fully 3D time-of-flight (TOF) PET scanners offer the potential of previously unachievable image quality in clinical PET imaging. TOF measurements add another degree of redundancy and make count-limited TOF-PET imaging more robust. The data space for 3D TOF-PET data is five dimensional with two degrees of redundancy. Previously, consistency equations were used to characterize the redundancy of TOF-PET data. In this paper, we first derive two Fourier consistency equations and the Fourier-John equation for 3D TOF PET based on the generalized projection-slice theorem; the three partial differential equations (PDEs) are the dual of the sinogram consistency equations and John's equation. We then solve the three PDEs using the method of characteristics. The two degrees of entangled redundancy of TOF-PET data can be explicitly elicited and exploited by the solutions of the PDEs along the characteristic curves, which gives a complete understanding of the rich structure of the 3D X-ray transform with TOF measurements. Fourier rebinning equations and other mapping equations among different types of PET data are special cases of the general solutions. We also obtain new Fourier rebinning and consistency (FORCE) equations from other special cases of the general solutions, and thus we obtain a complete scheme to convert among different types of PET data: 3D TOF, 3D non-TOF, 2D TOF and 2D non-TOF PET data. The new FORCE equations can be used as new Fourier rebinning algorithms for TOF-PET data reduction, or inverse rebinnings for designing fast projectors, or consistency conditions for estimating missing data. Finally, we give a numerical example for a 2D TOF PET to show the efficacy of the unified Fourier solutions.

(10:45) M6B1-2, Joint Activity and Attenuation Reconstruction of Listmode TOF-PET Data

A. Rezaei1, M. Bickell1, R. Fulton2, J. Nuyts1

1Nuclear Medicine, KU Leuven, Leuven, Belgium
2Brain and Mind Research Institute, Faculty of Health Sciences, University of Sydney, Sydney, Australia
Different methods have been proposed for simultaneous reconstruction of activity and attenuation from TOF-PET sinogram data. In this work we present the listmode maximum likelihood activity and attenuation reconstruction (MLAA) and the listmode maximum likelihood attenuation correction factors (MLACF) algorithms building on their established sinogram implementation. Our listmode MLAA differs from a recently proposed listmode algorithm by incorporating the maximum likelihood transmission reconstruction (MLTR) algorithm in MLAA which is a similar reconstruction algorithm to the listmode Image Based Reconstruction Algorithm (ISRA) for emission tomography. We investigate the reconstruction results on a scan of the NEMA IEC body phantom.

(11:00) M6B1-3, A Monotonic Image-Space Algorithm for Joint PET Image Reconstruction and Motion Estimation

G. Wang, J. Qi

University of California, Davis, CA, USA
Motion compensation in PET imaging has become more and more important for obtaining high-resolution images. PET emission image and patient motion can be estimated simultaneously from gated data through a joint estimation framework. The resulting optimization problem, however, is challenging to solve. We propose an efficient algorithm for joint estimation by using the optimization transfer with the expectation maximization (EM) surrogate function. Each iteration of the algorithm consists of three separable steps: a gated image reconstruction by the EM update, motion estimation by image registration and image fusion with motion compensation. This algorithm resembles an empirical image-space approach, but is guaranteed to converge monotonically. Results from a computer simulation showed the proposed algorithm is faster than an existing monotonic gradient algorithm and is more stable than its nonmonotonic variant.

(11:15) M6B1-4, Joint Reconstruction of Activity and Attenuation Using MR-Based Priors: Application to Clinical TOF PET/MR

S. Ahn1, L. Cheng1, D. Shanbhag2, F. Wiesinger3, R. Manjeshwar1

1GE Global Research, Niskayuna, NY, USA
2GE Global Research, Bangalore, India
3GE Global Research, Munich, Germany
Attenuation correction is critical to accurate PET quantitation. However, it is challenging to extract accurate information on attenuation from MR images because of distinct physics of MR and PET. The goal is to achieve robust and accurate attenuation correction in PET/MR. To this end, we synergistically combine 1) the approach of joint reconstruction of activity and attenuation and 2) the MR-segmentation based attenuation correction. We use the MR-segmentation based attenuation map as a MR-based prior when jointly reconstructing the activity image and the attenuation map. We evaluate the combined approach on TOF PET/MR clinical data and demonstrate that the joint reconstruction approach with MR-based priors can recover the attenuation of metal implants, internal air cavities and bones in a robust way.

(11:30) M6B1-5, Event-by-Event Respiratory Motion Correction for Dynamic PET Imaging

Y. Yu1,2,3, C. Chan1, T. Ma2,3, J.-D. Gallezot1, M. Naganawa1, O. J. Kelada4,5, M. Germino6, R. E. Carson1,6, C. Liu1,6

1Department of Diagnostic Radiology, Yale University, New Haven, CT, United States
2Department of Engineering Physics, Tsinghua University, Beijing, China
3Ministry of Education (Tsinghua University), Key Laboratory of Particle & Radiation Imaging, Beijing, China
4Department of Therapeutic Radiology, Yale University School of Medicine, New Haven, CT, United States
5Department of Medical Physics in Radiation Oncology, German Cancer Research Center, Heidelberg, Germany
6Department of Biomedical Engineering, Yale University School of Medicine, New Haven, CT, United States
Existing respiratory motion correction methods typically are only applicable to static PET imaging. We have previously developed an event-by-event respiratory motion correction method utilizing correlations between Internal organ motion and External respiratory signal (INTEX3D), which is uniquely capable of correcting respiratory for dynamic imaging. In this study, we applied INTEX3D to human dynamic PET studies with various tracers. Quantification of kinetic parameter estimation was investigated. In this study,eight human subjects with three tracers were investigated including: pancreatic beta cell tracer [18F]FP(+)DTBZ (n=4), tumor hypoxia tracer [18F]fluoromisonidazole (FMISO) (n=1), and myocardial perfusion tracer Rb-82 (n=3, rest and stress). 3D internal organ motion at high temporal resolution was obtained by INTEX3D to guide event-by-event respiratory motion correction in each dynamic frame. Time activity curves of Regions of Interest drawn on end-expiration PET images were obtained. Total volume of distribution (VT) and Ki were estimated with arterial input functions by MA1 model for [18F]FP(+)DTBZ and 2-tissue irreversible model(2Ti) for FMISO respectively. For Rb-82 studies, K1 was obtained with the 1-tissue model using left-ventricle image derived input-function and rest/stress blood flow and coronary flow reserve were calculated. With INTEX3D correction, VT for [18F]FP(+)DTBZ, Ki for FMISO, and K1 for Rb-82 stress studies increased by 17%±6%, 20% and 29%±13% respectively. The standard errors were reduced by 28%, 10% and 7%. Larger motion amplitudes and K1 increases were observed in Rb stress studies than rest. Coronary flow reserve increased by 62±25% in average after motion correction. INTEX3D method substantially changed the estimated parameters from dynamic PET with various tracers. Thus, correction for respiratory motion is important for accurate quantification from dynamic PET.

(11:45) M6B1-6, Development and Evaluation of Four PET Image-Based Dual Respiratory and Cardiac Motion Estimation Methods

T. Feng, J. Wang, B. M. W. Tsui

Johns Hopkins University, MD, USA
We have previously shown 4D image reconstructions with motion compensation using accurate model of dual respiratory and cardiac (R&C) motions provides much improved 4D cardiac gated image qualities. The goal of this study is to develop and evaluate 4 R&C motion vector field (MVF) estimation methods based on the improved 4D PET images. In Method 1, the dual R&C motions are estimated directly from the dual R&C gated images. In Methods 2, 3 and 4, they are estimated indirectly by estimating the respiratory motion (RM) and cardiac motion (CM) separately from the respiratory gated only and cardiac gated only images. Methods 3 also models the effects of RM on CM estimation by applying an image-based RM correction on the cardiac gated images while Methods 4 iteratively models the mutual effects of RM and CM estimations. Realistic and almost noise-free PET projection data were generated from the 4D XCAT phantom with realistic and known R&C MVF using Monte Carlo simulation. They were subsequently scaled and were added Poisson noise to generate additional datasets with 2 more different noise levels, and were reconstructed using a 4D image reconstruction method to obtain dual R&C gated images. The four dual R&C MVF estimation methods were applied to the dual R&C gated images and the estimated MVFs were compared to the known R&C MVFs. The resultant MVFs show that among the 4 estimation methods, Methods 2 performed the worst for noise-free case while Method 1 performed the worst for noisy cases in terms of the average mean-squared-errors (MSEs) between estimated and known MVFs. Methods 4 and 3 showed comparable results and provide reduced MSE by up to 35% of that in Method 1 for noisy cases. We have developed and evaluated 4 different R&C MVF estimation methods for use in 4D PET image reconstruction with accurate motion correction and found separate R&C estimation with modeling of RM on CM estimation (Method 3) to be the best option for accurate estimation of dual R&C motion.

(12:00) M6B1-7, TOF Data Non-Rigid Motion Correction

V. Y. Panin, H. Bal

Molecular Imaging, Siemens Healthcare, Knoxville, TN, USA
PET acquisition requires prolonged scan times, and during the scan a large magnitude patient motion can occur. Breathing may result in a significant displacement of organs and consequent blurring of clinically relevant features. Various non-rigid motion corrections that act in the image space were proposed to address this problem. TOF data can be considered to be histo-images. Therefore, non-rigid motion correction can be performed in this quasi image space. The TOF locality property can be used to locally perform motion correction; that is, the approximation of motion as locally rigid on a scale of TOF resolution. In this work we investigate motion correction in the TOF data space, assuming a known motion field. Data correction factors, such as normalization and attenuation, will be combined for motion compensation depending on the combination of data. The benefit of the presented motion correction is that only one data set needs to be used for the final reconstruction. An XCAT phantom is used in computer simulations. Initial results showed that the presented methodology accommodates for changes in non-rigid body movements for a typical pattern of patient motion.

(12:15) M6B1-8, Image-Based Modeling of PSF Deformation with Application to Limited Angle PET Data

S. Matej, Y. Li, J. Panetta, J. S. Karp, S. Surti

Radiology, University of Pennsylvania, Philadelphia, PA, USA
The point-spread-functions (PSFs) of reconstructed images can be deformed due to the detector properties, such as the resolution and depth-of-interaction effects, and data geometries, such as the limited angular coverage in dual-panel systems. The PSF deformations cause decreased quantitative accuracy and consistency of the uptake measurements across the field of view. While reconstruction models of the detectors and acquisition process provide improvement in the lesion uptake measurements and uniformity in general, for the limited angle data, or for imperfect reconstruction models, the reconstructed image will still be distorted and in a spatially variant way, thus affecting the quantitative results. We are proposing to use image-based resolution model (IRM) to include such image PSF deformation effects. Originally the IRM was mostly used for approximating data resolution effects in a computationally efficient way, but recently it was also used to mitigate effects of simplified geometric projectors. Our work goes beyond this by including into the IRM reconstruction imperfections caused by the limited angle data and any other (residual) deformation effects. We applied and tested these concepts for a dedicated breast imaging geometry (B-PET) consisting of dual-panel TOF detectors. In this feasibility study, we compared simple spatially invariant approximation to the PSF deformation (by capturing only its general elongation through elongated 3D Gaussian) with the spatially variant model using Gaussian mixture model more accurately capturing asymmetry and shape of the deformed PSF in the simulated B-PET scanner. We tested reconstructions with those models for lesions located at various spatial locations. Results illustrate ability of the IRM to suppress the PSF deformation effects and decrease the overall uptake bias in the reconstruction when using the proposed PSF-based model, and especially making the results more robust independent of the location within the FOV.