A simple regularizer for B-spline nonrigid image registration that encourages local invertibility

Deep Learning Based Joint PET Image Reconstruction and Motion Estimation

Respiratory motion is one of the main sources of motion artifacts in positron emission tomography (PET) imaging. The emission image and patient motion can be estimated simultaneously from respiratory gated data through a joint estimation framework. However, conventional motion estimation methods based on registration of a pair of images are sensitive to noise. The goal of this study is to develop a robust joint estimation method that incorporates a deep learning (DL)-based image registration approach for motion estimation. We propose a joint estimation framework by incorporating a learned image registration network into a regularized PET image reconstruction. The joint estimation was formulated as a constrained optimization problem with moving gated images related to a fixed image via the deep neural network. The constrained optimization problem is solved by the alternating direction method of multipliers (ADMM) algorithm. The effectiveness of the algorithm was demonstrated using simulated and real data. We compared the proposed DL-ADMM joint estimation algorithm with a monotonic iterative joint estimation. Motion compensated reconstructions using pre-calculated deformation fields by DL-based (DL-MC recon) and iterative (iterative-MC recon) image registration were also included for comparison. Our simulation study shows that the proposed DL-ADMM joint estimation method reduces bias compared to the ungated image without increasing noise and outperforms the competing methods. In the real data study, our proposed method also generated higher lesion contrast and sharper liver boundaries compared to the ungated image and had lower noise than the reference gated image.

A generalized framework for analytic regularization of uniform cubic B-spline displacement fields

Image registration is an inherently ill-posed problem that lacks the constraints needed for a unique mapping between voxels of the two images being registered. As such, one must regularize the registration to achieve physically meaningful transforms. The regularization penalty is usually a function of derivatives of the displacement-vector field and can be calculated either analytically or numerically. The numerical approach, however, is computationally expensive depending on the image size, and therefore a computationally efficient analytical framework has been developed. Using cubic B-splines as the registration transform, we develop a generalized mathematical framework that supports five distinct regularizers: diffusion, curvature, linear elastic, third-order, and total displacement. We validate our approach by comparing each with its numerical counterpart in terms of accuracy. We also provide benchmarking results showing that the analytic solutions run significantly faster-up to two orders of magnitude-than finite differencing based numerical implementations.

Fast 4D elastic group-wise image registration. Convolutional interpolation revisited

BACKGROUND AND OBJECTIVE

This paper proposes a new and highly efficient implementation of 3D+t groupwise registration based on the free-form deformation paradigm.

METHODS

Deformation is posed as a cascade of 1D convolutions, achieving great reduction in execution time for evaluation of transformations and gradients.

RESULTS

The proposed method has been applied to 4D cardiac MRI and 4D thoracic CT monomodal datasets. Results show an average runtime reduction above 90%, both in CPU and GPU executions, compared with the classical tensor product formulation.

CONCLUSIONS

Our implementation, although fully developed for the metric sum of squared differences, can be extended to other metrics and its adaptation to multiresolution strategies is straightforward. Therefore, it can be extremely useful to speed up image registration procedures in different applications where high dimensional data are involved.

Motion correction for PET data using subspace-based real-time MR imaging in simultaneous PET/MR

Image quality of positron emission tomography (PET) reconstructions is degraded by subject motion occurring during the acquisition. Magnetic resonance (MR)-based motion correction approaches have been studied for PET/MR scanners and have been successful at capturing regular motion patterns, when used in conjunction with surrogate signals (e.g. navigators) to detect motion. However, handling irregular respiratory motion and bulk motion remains challenging. In this work, we propose an MR-based motion correction method relying on subspace-based real-time MR imaging to estimate motion fields used to correct PET reconstructions. We take advantage of the low-rank characteristics of dynamic MR images to reconstruct high-resolution MR images at high frame rates from highly undersampled k-space data. Reconstructed dynamic MR images are used to determine motion phases for PET reconstruction and estimate phase-to-phase nonrigid motion fields able to capture complex motion patterns such as irregular respiratory and bulk motion. MR-derived binning and motion fields are used for PET reconstruction to generate motion-corrected PET images. The proposed method was evaluated on in vivo data with irregular motion patterns. MR reconstructions accurately captured motion, outperforming state-of-the-art dynamic MR reconstruction techniques. Evaluation of PET reconstructions demonstrated the benefits of the proposed method in terms of motion artifacts reduction, improving the contrast-to-noise ratio by up to a factor 3 and achieveing a target-to-background ratio up to 90% superior compared to standard/uncorrected methods. The proposed method can improve the image quality of motion-corrected PET reconstructions in clinical applications.

Motion correction of respiratory-gated PET images using deep learning based image registration framework

Artifacts caused by patient breathing and movement during PET data acquisition affect image quality. Respiratory gating is commonly used to gate the list-mode PET data into multiple bins over a respiratory cycle. Non-rigid registration of respiratory-gated PET images can reduce motion artifacts and preserve count statistics, but it is time consuming. In this work, we propose an unsupervised non-rigid image registration framework using deep learning for motion correction. Our network uses a differentiable spatial transformer layer to warp the moving image to the fixed image and uses a stacked structure for deformation field refinement. Estimated deformation fields were incorporated into an iterative image reconstruction algorithm to perform motion compensated PET image reconstruction. We validated the proposed method using simulation and clinical data and implemented an iterative image registration approach for comparison. Motion compensated reconstructions were compared with ungated images. Our simulation study showed that the motion compensated methods can generate images with sharp boundaries and reveal more details in the heart region compared with the ungated image. The resulting normalized root mean square error (NRMS) was 24.3 ± 1.7% for the deep learning based motion correction, 31.1 ± 1.4% for the iterative registration based motion correction, and 41.9 ± 2.0% for ungated reconstruction. The proposed deep learning based motion correction reduced the bias compared with the ungated image without increasing the noise level and outperformed the iterative registration based method. In the real data study, both motion compensated images provided higher lesion contrast and sharper liver boundaries than the ungated image and had lower noise than the reference gate image. The contrast of the proposed method based on the deep neural network was higher than the ungated image and iterative registration method at any matched noise level.

MR-based cardiac and respiratory motion correction of PET: application to static and dynamic cardiac 18F-FDG imaging

Motion of the myocardium deteriorates the quality and quantitative accuracy of cardiac PET images. We present a method for MR-based cardiac and respiratory motion correction of cardiac PET data and evaluate its impact on estimation of activity and kinetic parameters in human subjects. Three healthy subjects underwent simultaneous dynamic ¹⁸F-FDG PET and MRI on a hybrid PET/MR scanner. A cardiorespiratory motion field was determined for each subject using navigator, tagging and golden-angle radial MR acquisitions. Acquired coincidence events were binned into cardiac and respiratory phases using electrocardiogram and list mode-driven signals, respectively. Dynamic PET images were reconstructed with MR-based motion correction (MC) and without motion correction (NMC). Parametric images of ¹⁸F-FDG consumption rates (K_i) were estimated using Patlak's method for both MC and NMC images. MC alleviated motion artifacts in PET images, resulting in improved spatial resolution, improved recovery of activity in the myocardium wall and reduced spillover from the myocardium to the left ventricle cavity. Significantly higher myocardium contrast-to-noise ratio and lower apparent wall thickness were obtained in MC versus NMC images. Likewise, parametric images of K_i calculated with MC data had improved spatial resolution as compared to those obtained with NMC. Consistent with an increase in reconstructed activity concentration in the frames used during kinetic analyses, MC led to the estimation of higher K_i values almost everywhere in the myocardium, with up to 18% increase (mean across subjects) in the septum as compared to NMC. This study shows that MR-based motion correction of cardiac PET results in improved image quality that can benefit both static and dynamic studies.

Real-Time Filtering with Sparse Variations for Head Motion in Magnetic Resonance Imaging

Estimating a time-varying signal, such as head motion from magnetic resonance imaging data, becomes particularly challenging in the face of other temporal dynamics such as functional activation. This paper describes a new Kalman filter-like framework that includes a sparse residual term in the measurement model. This additional term allows the extended Kalman filter to generate real-time motion estimates suitable for prospective motion correction when such dynamics occur. An iterative augmented Lagrangian algorithm similar to the alterating direction method of multipliers implements the update step for this Kalman filter. This paper evaluates the accuracy and convergence rate of this iterative method for small and large motion in terms of its sensitivity to parameter selection. The included experiment on a simulated functional magnetic resonance imaging acquisition demonstrates that the resulting method improves the maximum Youden's J index of the time series analysis by 2-3% versus retrospective motion correction, while the sensitivity index increases from 4.3 to 5.4 when combining prospective and retrospective correction.

Motion-compensated reconstruction of magnetic resonance images from undersampled data

Magnetic resonance imaging of patients who find difficulty lying still or holding their breath can be challenging. Unresolved intra-frame motion yields blurring artifacts and limits spatial resolution. To correct for intra-frame non-rigid motion, such as in pediatric body imaging, this paper describes a multi-scale technique for joint estimation of the motion occurring during the acquisition and of the desired uncorrupted image. This technique regularizes the motion coefficients to enforce invertibility and minimize numerical instability. This multi-scale approach takes advantage of variable-density sampling patterns used in accelerated imaging to resolve large motion from a coarse scale. The resulting method improves image quality for a set of two-dimensional reconstructions from data simulated with independently generated deformations, with statistically significant increases in both peak signal to error ratio and structural similarity index. These improvements are consistent across varying undersampling factors and severities of motion and take advantage of the variable density sampling pattern.

Magnetic Resonance-based Motion Correction for Quantitative PET in Simultaneous PET-MR Imaging

Motion degrades image quality and quantitation of PET images, and is an obstacle to quantitative PET imaging. Simultaneous PET-MR offers a tool that can be used for correcting the motion in PET images by using anatomic information from MR imaging acquired concurrently. Motion correction can be performed by transforming a set of reconstructed PET images into the same frame or by incorporating the transformation into the system model and reconstructing the motion-corrected image. Several phantom and patient studies have validated that MR-based motion correction strategies have great promise for quantitative PET imaging in simultaneous PET-MR.

Local All-Pass Geometric Deformations

This paper deals with the estimation of a deformation that describes the geometric transformation between two images. To solve this problem, we propose a novel framework that relies upon the brightness consistency hypothesis-a pixel's intensity is maintained throughout the transformation. Instead of assuming small distortion and linearizing the problem (e.g. via Taylor Series expansion), we propose to interpret the brightness hypothesis as an all-pass filtering relation between the two images. The key advantages of this new interpretation are that no restrictions are placed on the amplitude of the deformation or on the spatial variations of the images. Moreover, by converting the all-pass filtering to a linear forward-backward filtering relation, our solution to the estimation problem equates to solving a linear system of equations, which leads to a highly efficient implementation. Using this framework, we develop a fast algorithm that relates one image to another, on a local level, using an all-pass filter and then extracts the deformation from the filter-hence the name "Local All-Pass" (LAP) algorithm. The effectiveness of this algorithm is demonstrated on a variety of synthetic and real deformations that are found in applications, such as image registration and motion estimation. In particular, when compared with a selection of image registration algorithms, the LAP obtains very accurate results for significantly reduced computation time and is very robust to noise corruption.

Randomly Perturbed B-Splines for Nonrigid Image Registration

B-splines are commonly utilized to construct the transformation model in free-form deformation (FFD) based registration. B-splines become smoother with increasing spline order. However, a higher-order B-spline requires a larger support region involving more control points, which means higher computational cost. In general, the third-order B-spline is considered as a good compromise between spline smoothness and computational cost. A lower-order function is seldom used to construct the transformation model for registration since it is less smooth. In this research, we investigated whether lower-order B-spline functions can be utilized for more efficient registration, while preserving smoothness of the deformation by using a novel random perturbation technique. With the proposed perturbation technique, the expected value of the cost function given probability density function (PDF) of the perturbation is minimized by a stochastic gradient descent optimization. Extensive experiments on 2D synthetically deformed brain images, and real 3D lung and brain scans demonstrated that the novel randomly perturbed free-form deformation (RPFFD) approach improves the registration accuracy and transformation smoothness. Meanwhile, lower-order RPFFD methods reduce the computational cost substantially.

Adaptive radiotherapy for NSCLC patients: utilizing the principle of energy conservation to evaluate dose mapping operations

Tumor regression during the course of fractionated radiotherapy confounds the ability to accurately estimate the total dose delivered to tumor targets. Here we present a new criterion to improve the accuracy of image intensity-based dose mapping operations for adaptive radiotherapy for patients with non-small cell lung cancer (NSCLC). Six NSCLC patients were retrospectively investigated in this study. An image intensity-based B-spline registration algorithm was used for deformable image registration (DIR) of weekly CBCT images to a reference image. The resultant displacement vector fields were employed to map the doses calculated on weekly images to the reference image. The concept of energy conservation was introduced as a criterion to evaluate the accuracy of the dose mapping operations. A finite element method (FEM)-based mechanical model was implemented to improve the performance of the B-Spline-based registration algorithm in regions involving tumor regression. For the six patients, deformed tumor volumes changed by 21.2  ±  15.0% and 4.1  ±  3.7% on average for the B-Spline and the FEM-based registrations performed from fraction 1 to fraction 21, respectively. The energy deposited in the gross tumor volume (GTV) was 0.66 Joules (J) per fraction on average. The energy derived from the fractional dose reconstructed by the B-spline and FEM-based DIR algorithms in the deformed GTV's was 0.51 J and 0.64 J, respectively. Based on landmark comparisons for the 6 patients, mean error for the FEM-based DIR algorithm was 2.5  ±  1.9 mm. The cross-correlation coefficient between the landmark-measured displacement error and the loss of radiation energy was  -0.16 for the FEM-based algorithm. To avoid uncertainties in measuring distorted landmarks, the B-Spline-based registrations were compared to the FEM registrations, and their displacement differences equal 4.2  ±  4.7 mm on average. The displacement differences were correlated to their relative loss of radiation energy with a cross-correlation coefficient equal to 0.68. Based on the principle of energy conservation, the FEM-based mechanical model has a better performance than the B-Spline-based DIR algorithm. It is recommended that the principle of energy conservation be incorporated into a comprehensive QA protocol for adaptive radiotherapy.

Transformation diffusion reconstruction of three-dimensional histology volumes from two-dimensional image stacks

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A method for 3D reconstruction of serial 2D histology image stacks is proposed.

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Pre-alignment to an external pre-cut reference (blockface) prevents shape artifacts.

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Formulated as diffusion of transformations from each slice to its neighbors.

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Registrations replaced by much faster transformation operations.

Traditional histology is the gold standard for tissue studies, but it is intrinsically reliant on two-dimensional (2D) images. Study of volumetric tissue samples such as whole hearts produces a stack of misaligned and distorted 2D images that need to be reconstructed to recover a congruent volume with the original sample's shape. In this paper, we develop a mathematical framework called Transformation Diffusion (TD) for stack alignment refinement as a solution to the heat diffusion equation. This general framework does not require contour segmentation, is independent of the registration method used, and is trivially parallelizable. After the first stack sweep, we also replace registration operations by operations in the space of transformations, several orders of magnitude faster and less memory-consuming. Implementing TD with operations in the space of transformations produces our Transformation Diffusion Reconstruction (TDR) algorithm, applicable to general transformations that are closed under inversion and composition. In particular, we provide formulas for translation and affine transformations. We also propose an Approximated TDR (ATDR) algorithm that extends the same principles to tensor-product B-spline transformations. Using TDR and ATDR, we reconstruct a full mouse heart at pixel size 0.92 µm × 0.92 µm, cut 10 µm thick, spaced 20 µm (84G). Our algorithms employ only local information from transformations between neighboring slices, but the TD framework allows theoretical analysis of the refinement as applying a global Gaussian low-pass filter to the unknown stack misalignments. We also show that reconstruction without an external reference produces large shape artifacts in a cardiac specimen while still optimizing slice-to-slice alignment. To overcome this problem, we use a pre-cutting blockface imaging process previously developed by our group that takes advantage of Brewster's angle and a polarizer to capture the outline of only the topmost layer of wax in the block containing embedded tissue for histological sectioning.

Impact of motion and partial volume effects correction on PET myocardial perfusion imaging using simultaneous PET-MR

PET is an established modality for myocardial perfusion imaging (MPI) which enables quantification of absolute myocardial blood flow (MBF) using dynamic imaging and kinetic modeling. However, heart motion and partial volume effects (PVE) significantly limit the spatial resolution and quantitative accuracy of PET MPI. Simultaneous PET-MR offers a solution to the motion problem in PET by enabling MR-based motion correction of PET data. The aim of this study was to develop a motion and PVE correction methodology for PET MPI using simultaneous PET-MR, and to assess its impact on both static and dynamic PET MPI using 18F-Flurpiridaz, a novel 18F-labeled perfusion tracer. Two dynamic 18F-Flurpiridaz MPI scans were performed on healthy pigs using a PET-MR scanner. Cardiac motion was tracked using a dedicated tagged-MRI (tMR) sequence. Motion fields were estimated using non-rigid registration of tMR images and used to calculate motion-dependent attenuation maps. Motion correction of PET data was achieved by incorporating tMR-based motion fields and motion-dependent attenuation coefficients into image reconstruction. Dynamic and static PET datasets were created for each scan. Each dataset was reconstructed as (i) Ungated, (ii) Gated (end-diastolic phase), and (iii) Motion-Corrected (MoCo), each without and with point spread function (PSF) modeling for PVE correction. Myocardium-to-blood concentration ratios (MBR) and apparent wall thickness were calculated to assess image quality for static MPI. For dynamic MPI, segment- and voxel-wise MBF values were estimated by non-linear fitting of a 2-tissue compartment model to tissue time-activity-curves. MoCo and Gating respectively decreased mean apparent wall thickness by 15.1% and 14.4% and increased MBR by 20.3% and 13.6% compared to Ungated images (P  <  0.01). Combined motion and PSF correction (MoCo-PSF) yielded 30.9% (15.7%) lower wall thickness and 82.2% (20.5%) higher MBR compared to Ungated data reconstructed without (with) PSF modeling (P  <  0.01). For dynamic PET, mean MBF across all segments were comparable for MoCo (0.72  ±  0.21 ml/min/ml) and Gating (0.69  ±  0.18 ml/min/ml). Ungated data yielded significantly lower mean MBF (0.59  ±  0.16 ml/min/ml). Mean MBF for MoCo-PSF was 0.80  ±  0.22 ml/min/ml, which was 37.9% (25.0%) higher than that obtained from Ungated data without (with) PSF correction (P  <  0.01). The developed methodology holds promise to improve the image quality and sensitivity of PET MPI studies performed using PET-MR.

Co-registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization

Diffusion MRI provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain. Echo planar imaging (EPI) sequences, which are frequently used for acquisition of diffusion images, are sensitive to inhomogeneities in the primary magnetic (B0) field that cause localized distortions in the reconstructed images. We describe and evaluate a new method for correction of susceptibility-induced distortion in diffusion images in the absence of an accurate B0 fieldmap. In our method, the distortion field is estimated using a constrained non-rigid registration between an undistorted T1-weighted anatomical image and one of the distorted EPI images from diffusion acquisition. Our registration framework is based on a new approach, INVERSION (Inverse contrast Normalization for VERy Simple registratION), which exploits the inverted contrast relationship between T1- and T2-weighted brain images to define a simple and robust similarity measure. We also describe how INVERSION can be used for rigid alignment of diffusion images and T1-weighted anatomical images. Our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters. Compared to other methods, INVERSION shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non-rigid distortion correction.

Accelerated acquisition of tagged MRI for cardiac motion correction in simultaneous PET-MR: phantom and patient studies

PURPOSE

Degradation of image quality caused by cardiac and respiratory motions hampers the diagnostic quality of cardiac PET. It has been shown that improved diagnostic accuracy of myocardial defect can be achieved by tagged MR (tMR) based PET motion correction using simultaneous PET-MR. However, one major hurdle for the adoption of tMR-based PET motion correction in the PET-MR routine is the long acquisition time needed for the collection of fully sampled tMR data. In this work, the authors propose an accelerated tMR acquisition strategy using parallel imaging and/or compressed sensing and assess the impact on the tMR-based motion corrected PET using phantom and patient data.

METHODS

Fully sampled tMR data were acquired simultaneously with PET list-mode data on two simultaneous PET-MR scanners for a cardiac phantom and a patient. Parallel imaging and compressed sensing were retrospectively performed by GRAPPA and kt-FOCUSS algorithms with various acceleration factors. Motion fields were estimated using nonrigid B-spline image registration from both the accelerated and fully sampled tMR images. The motion fields were incorporated into a motion corrected ordered subset expectation maximization reconstruction algorithm with motion-dependent attenuation correction.

RESULTS

Although tMR acceleration introduced image artifacts into the tMR images for both phantom and patient data, motion corrected PET images yielded similar image quality as those obtained using the fully sampled tMR images for low to moderate acceleration factors (<4). Quantitative analysis of myocardial defect contrast over ten independent noise realizations showed similar results. It was further observed that although the image quality of the motion corrected PET images deteriorates for high acceleration factors, the images were still superior to the images reconstructed without motion correction.

CONCLUSIONS

Accelerated tMR images obtained with more than 4 times acceleration can still provide relatively accurate motion fields and yield tMR-based motion corrected PET images with similar image quality as those reconstructed using fully sampled tMR data. The reduction of tMR acquisition time makes it more compatible with routine clinical cardiac PET-MR studies.

Deformation corrected compressed sensing (DC-CS): a novel framework for accelerated dynamic MRI

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover contrast enhanced dynamic magnetic resonance images from undersampled measurements. We introduce a formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage-based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to reduce the risk of convergence to local minima. The decoupling enabled by the proposed scheme enables us to apply this scheme to contrast enhanced MRI applications. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we observe superior image quality of the proposed DC-CS scheme in comparison to the classical k-t FOCUSS with motion estimation/correction scheme, and demonstrate reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation uncorrected signal.

Relative role of motion and PSF compensation in whole-body oncologic PET-MR imaging

PURPOSE

Respiratory motion and partial-volume effects are the two main sources of image degradation in whole-body PET imaging. Simultaneous PET-MR allows measurement of respiratory motion using MRI while collecting PET events. Improved PET images may be obtained by modeling respiratory motion and point spread function (PSF) within the PET iterative reconstruction process. In this study, the authors assessed the relative impact of PSF modeling and MR-based respiratory motion correction in phantoms and patient studies using a whole-body PET-MR scanner.

METHODS

An asymmetric exponential PSF model accounting for radially varying and axial detector blurring effects was obtained from point source acquisitions performed in the PET-MR scanner. A dedicated MRI acquisition protocol using single-slice steady state free-precession MR acquisitions interleaved with pencil-beam navigator echoes was developed to track respiratory motion during PET-MR studies. An iterative ordinary Poisson fully 3D OSEM PET reconstruction algorithm modeling all the physical effects of the acquisition (attenuation, scatters, random events, detectors efficiencies, PSF), as well as MR-based nonrigid respiratory deformations of tissues (in both emission and attenuation maps) was developed. Phantom and(18)F-FDG PET-MR patient studies were performed to evaluate the proposed quantitative PET-MR methods.

RESULTS

The phantom experiment results showed that PSF modeling significantly improved contrast recovery while limiting noise propagation in the reconstruction process. In patients with soft-tissue static lesions, PSF modeling improved lesion contrast by 19.7%-109%, enhancing the detectability and assessment of small tumor foci. In a patient study with small moving hepatic lesions, the proposed reconstruction technique improved lesion contrast by 54.4%-98.1% and reduced apparent lesion size by 21.8%-34.2%. Improvements were particularly important for the smallest lesion undergoing large motion at the lung-liver interface. Heterogeneous tumor structures delineation was substantially improved. Enhancements offered by PSF modeling were more important when correcting for motion at the same time.

CONCLUSIONS

The results suggest that the proposed quantitative PET-MR methods can significantly enhance the performance of tumor diagnosis and staging as compared to conventional methods. This approach may enable utilization of the full potential of the scanner in oncologic studies of both the lower abdomen, with moving lesions, as well as other parts of the body unaffected by motion.

Simple and efficient approach for restoration of non-uniformly warped images

A high accuracy image dewarping method is proposed to restore images from non-uniformly warped video sequences degraded by atmospheric turbulence. This approach contains three major steps. First, a non-rigid image registration technique is employed to register all the frames in the sequence to a reference frame and estimate the motion fields. Second, an iterative First Register Then Average And Subtract (iFRTAAS) method is applied to correct the geometric deformations of the warped frames. The third step involves applying a non-local means filter for the compensation of noise and to improve the signal-to-noise ratio (SNR) of the restored reference frame. Simulations are carried out by applying the method to synthetic and real-life turbulence degraded videos and by determining various quality metrics. A performance comparison is presented between the proposed method and two earlier methods, which verifies that the proposed method provides significant improvement on the image restoration accuracy.

Deformable image registration with local rigidity constraints for cone-beam CT-guided spine surgery

Image-guided spine surgery (IGSS) is associated with reduced co-morbidity and improved surgical outcome. However, precise localization of target anatomy and adjacent nerves and vessels relative to planning information (e.g., device trajectories) can be challenged by anatomical deformation. Rigid registration alone fails to account for deformation associated with changes in spine curvature, and conventional deformable registration fails to account for rigidity of the vertebrae, causing unrealistic distortions in the registered image that can confound high-precision surgery. We developed and evaluated a deformable registration method capable of preserving rigidity of bones while resolving the deformation of surrounding soft tissue. The method aligns preoperative CT to intraoperative cone-beam CT (CBCT) using free-form deformation (FFD) with constraints on rigid body motion imposed according to a simple intensity threshold of bone intensities. The constraints enforced three properties of a rigid transformation-namely, constraints on affinity (AC), orthogonality (OC), and properness (PC). The method also incorporated an injectivity constraint (IC) to preserve topology. Physical experiments involving phantoms, an ovine spine, and a human cadaver as well as digital simulations were performed to evaluate the sensitivity to registration parameters, preservation of rigid body morphology, and overall registration accuracy of constrained FFD in comparison to conventional unconstrained FFD (uFFD) and Demons registration. FFD with orthogonality and injectivity constraints (denoted FFD+OC+IC) demonstrated improved performance compared to uFFD and Demons. Affinity and properness constraints offered little or no additional improvement. The FFD+OC+IC method preserved rigid body morphology at near-ideal values of zero dilatation (D = 0.05, compared to 0.39 and 0.56 for uFFD and Demons, respectively) and shear (S = 0.08, compared to 0.36 and 0.44 for uFFD and Demons, respectively). Target registration error (TRE) was similarly improved for FFD+OC+IC (0.7 mm), compared to 1.4 and 1.8 mm for uFFD and Demons. Results were validated in human cadaver studies using CT and CBCT images, with FFD+OC+IC providing excellent preservation of rigid morphology and equivalent or improved TRE. The approach therefore overcomes distortions intrinsic to uFFD and could better facilitate high-precision IGSS.

Towards coronary plaque imaging using simultaneous PET-MR: a simulation study

Coronary atherosclerotic plaque rupture is the main cause of myocardial infarction and the leading killer in the US. Inflammation is a known bio-marker of plaque vulnerability and can be assessed non-invasively using fluorodeoxyglucose-positron emission tomography imaging (FDG-PET). However, cardiac and respiratory motion of the heart makes PET detection of coronary plaque very challenging. Fat surrounding coronary arteries allows the use of MRI to track plaque motion during simultaneous PET-MR examination. In this study, we proposed and assessed the performance of a fat-MR based coronary motion correction technique for improved FDG-PET coronary plaque imaging in simultaneous PET-MR. The proposed methods were evaluated in a realistic four-dimensional PET-MR simulation study obtained by combining patient water-fat separated MRI and XCAT anthropomorphic phantom. Five small lesions were digitally inserted inside the patients coronary vessels to mimic coronary atherosclerotic plaques. The heart of the XCAT phantom was digitally replaced with the patient's heart. Motion-dependent activity distributions, attenuation maps, and fat-MR volumes of the heart, were generated using the XCAT cardiac and respiratory motion fields. A full Monte Carlo simulation using Siemens mMR's geometry was performed for each motion phase. Cardiac/respiratory motion fields were estimated using non-rigid registration of the transformed fat-MR volumes and incorporated directly into the system matrix of PET reconstruction along with motion-dependent attenuation maps. The proposed motion correction method was compared to conventional PET reconstruction techniques such as no motion correction, cardiac gating, and dual cardiac-respiratory gating. Compared to uncorrected reconstructions, fat-MR based motion compensation yielded an average improvement of plaque-to-background contrast of 29.6%, 43.7%, 57.2%, and 70.6% for true plaque-to-blood ratios of 10, 15, 20 and 25:1, respectively. Channelized Hotelling observer (CHO) signal-to-noise ratio (SNR) was used to quantify plaque detectability. CHO-SNR improvement ranged from 105% to 128% for fat-MR-based motion correction as compared to no motion correction. Likewise, CHO-SNR improvement ranged from 348% to 396% as compared to both cardiac and dual cardiac-respiratory gating approaches. Based on this study, our approach, a fat-MR based motion correction for coronary plaque PET imaging using simultaneous PET-MR, offers great potential for clinical practice. The ultimate performance and limitation of our approach, however, must be fully evaluated in patient studies.

Bias atlases for segmentation-based PET attenuation correction using PET-CT and MR

This study was to obtain voxel-wise PET accuracy and precision using tissue-segmentation for attenuation correction. We applied multiple thresholds to the CTs of 23 patients to classify tissues. For six of the 23 patients, MR images were also acquired. The MR fat/in-phase ratio images were used for fat segmentation. Segmented tissue classes were used to create attenuation maps, which were used for attenuation correction in PET reconstruction. PET bias images were then computed using the PET reconstructed with the original CT as the reference. We registered the CTs for all the patients and transformed the corresponding bias images accordingly. We then obtained the mean and standard deviation bias atlas using all the registered bias images. Our CT-based study shows that four-class segmentation (air, lungs, fat, other tissues), which is available on most PET-MR scanners, yields 15.1%, 4.1%, 6.6%, and 12.9% RMSE bias in lungs, fat, non-fat soft-tissues, and bones, respectively. An accurate fat identification is achievable using fat/in-phase MR images. Furthermore, we have found that three-class segmentation (air, lungs, other tissues) yields less than 5% standard deviation of bias within the heart, liver, and kidneys. This implies that three-class segmentation can be sufficient to achieve small variation of bias for imaging these three organs. Finally, we have found that inter- and intra-patient lung density variations contribute almost equally to the overall standard deviation of bias within the lungs.

Simultaneous 99mTc-MDP/123I-MIBG tumor imaging using SPECT-CT: phantom and constructed patient studies

PURPOSE

Authors' goal is to evaluate the performance of simultaneous (99m)Tc-MDP/(123)I-MIBG tumor imaging with fast Monte-Carlo (MC) based joint iterative reconstruction as compared to sequential (99m)Tc-MDP and (123)I-MIBG tumor imaging.

METHODS

Noise-free (99m)Tc and (123)I SPECT projections were acquired separately using an anthropomorphic torso phantom modified to include a fillable tube around the lungs to mimic ribs. Additionally, (99m)Tc and (123)I projections were acquired separately using a 1-cm spherical "tumor" placed at various distances from one detector. Tumor-present data were generated by adding tumor projections to the torso phantom data, which were scaled to the total counts in typical clinical studies. Twenty-five noise realizations were generated by adding Poisson noise to the projection data for each radionuclide. Dual-radionuclide data were synthesized by summing the (99m)Tc and (123)I projections. Image reconstruction was performed using: (1) SR-OSEM, ordered subset expectation maximization (OSEM) without scatter correction (SC) using single-radionuclide (SR) data; (2) SR-MC-OSEM, OSEM with a fast MC-based SC using SR data; (3) DR-OSEM, OSEM without SC using dual-radionuclide (DR) data; and (4) DR-MC-JOSEM, joint OSEM with a fast MC-based SC using DR data. Ten (99m)Tc-MDP and ten (123)I-MIBG data sets, which had tumors mathematically inserted, were also used to evaluate the performance of authors' approach. For the phantom study, relative bias and relative standard deviation of tumor uptake were computed for each tumor using the tumor uptake in the noise-free single-radionuclide images, which were reconstructed by SR-MC-OSEM, as the gold standard. For both the phantom and constructed patient studies, mean contrast and standard deviation of contrast were computed for each tumor for both the single- and dual-radionuclide images. Additionally, contrast recovery was computed as the ratio between mean contrast and the mean contrast for SR-MC-OSEM.

RESULTS

For the phantom study, DR-MC-JOSEM yielded 2.7% on average relative bias of tumor uptake using the images, which were reconstructed from the noise-free SR data with SR-MC-OSEM, as the gold-standard. For both the phantom and constructed patient studies, DR-MC-JOSEM yielded 94.7% and 95.2% tumor contrast recovery on average using SR-MC-OSEM as the reference, in the phantom and constructed patient studies, respectively. DR-MC-JOSEM yielded comparable relative standard deviation of bias and standard deviation of contrast to SR-MC-OSEM.

CONCLUSIONS

Simultaneous (99m)Tc-MDP/(123)I-MIBG tumor imaging using authors' dual-radionuclide reconstruction approach yielded comparable image quality to sequential (99m)Tc-MDP and (123)I-MIBG imaging. For patients who need to undergo both scans, authors' approach offers perfectly registered dual-tracer images under identical conditions without compromising image quality, and reduces the imaging cost while increasing patient throughput.

Magnetic resonance-based motion correction for positron emission tomography imaging

Positron emission tomography (PET) image quality is limited by patient motion. Emission data are blurred owing to cardiac and/or respiratory motion. Although spatial resolution is 4 mm for standard clinical whole-body PET scanners, the effective resolution can be as low as 1 cm owing to motion. Additionally, the deformation of attenuation medium causes image artifacts. Previously, gating has been used to "freeze" the motion, but led to significantly increased noise level. Simultaneous PET/magnetic resonance (MR) modality offers a new way to perform PET motion correction. MR can be used to measure 3-dimensional motion fields, which can then be incorporated into the iterative PET reconstruction to obtain motion-corrected PET images. In this report, we present MR imaging techniques to acquire dynamic images, a nonrigid image registration algorithm to extract motion fields from acquired MR images, and a PET reconstruction algorithm with motion correction. We also present results from both phantom and in vivo animal PET/MR studies. We demonstrate that MR-based PET motion correction using simultaneous PET/MR improves image quality and lesion detectability compared with gating and no motion correction.

Cardiac motion compensation and resolution modeling in simultaneous PET-MR: a cardiac lesion detection study

Cardiac motion and partial volume effects (PVE) are two of the main causes of image degradation in cardiac PET. Motion generates artifacts and blurring while PVE lead to erroneous myocardial activity measurements. Newly available simultaneous PET-MR scanners offer new possibilities in cardiac imaging as MRI can assess wall contractility while collecting PET perfusion data. In this perspective, we develop a list-mode iterative reconstruction framework incorporating both tagged-MR derived non-rigid myocardial wall motion and position dependent detector point spread function (PSF) directly into the PET system matrix. In this manner, our algorithm performs both motion 'deblurring' and PSF deconvolution while reconstructing images with all available PET counts. The proposed methods are evaluated in a beating non-rigid cardiac phantom whose hot myocardial compartment contains small transmural and non-transmural cold defects. In order to accelerate imaging time, we investigate collecting full and half k-space tagged MR data to obtain tagged volumes that are registered using non-rigid B-spline registration to yield wall motion information. Our experimental results show that tagged-MR based motion correction yielded an improvement in defect/myocardium contrast recovery of 34-206% as compared to motion uncorrected studies. Likewise, lesion detectability improved by respectively 115-136% and 62-235% with MR-based motion compensation as compared to gating and no motion correction and made it possible to distinguish non-transmural from transmural defects, which has clinical significance given the inherent limitations of current single modality imaging in identifying the amount of residual ischemia. The incorporation of PSF modeling within the framework of MR-based motion compensation significantly improved defect/myocardium contrast recovery (5.1-8.5%, p < 0.01) and defect detectability (39-56%, p < 0.01). No statistical difference was found in PET contrast and lesion detectability based on motion fields obtained with half and full k-space tagged data.

Noise properties of motion-compensated tomographic image reconstruction methods

Motion-compensated image reconstruction (MCIR) methods incorporate motion models to improve image quality in the presence of motion. MCIR methods differ in terms of how they use motion information and they have been well studied separately. However, there have been less theoretical comparisions of different MCIR methods. This paper compares the theoretical noise properties of three popular MCIR methods assuming known nonrigid motion. We show the relationship among three MCIR methods-motion-compensated temporal regularization (MTR), the parametric motion model (PMM), and post-reconstruction motion correction (PMC)-for penalized weighted least square cases. These analyses show that PMM and MTR are matrix-weighted sums of all registered image frames, while PMC is a scalar-weighted sum. We further investigate the noise properties of MCIR methods with Poisson models and quadratic regularizers by deriving accurate and fast variance prediction formulas using an "analytical approach." These theoretical noise analyses show that the variances of PMM and MTR are lower than or comparable to the variance of PMC due to the statistical weighting. These analyses also facilitate comparisons of the noise properties of different MCIR methods, including the effects of different quadratic regularizers, the influence of the motion through its Jacobian determinant, and the effect of assuming that total activity is preserved. Two-dimensional positron emission tomography simulations demonstrate the theoretical results.

Spatial resolution properties of motion-compensated tomographic image reconstruction methods

Many motion-compensated image reconstruction (MCIR) methods have been proposed to correct for subject motion in medical imaging. MCIR methods incorporate motion models to improve image quality by reducing motion artifacts and noise. This paper analyzes the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to nonuniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic log-likelihoods (e.g., Poisson likelihood) and quadratic regularizers. This effect may lead to quantification errors in small or narrow structures (such as small lesions or rings) of reconstructed images. This paper proposes novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. Two-dimensional PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.

MRI-based nonrigid motion correction in simultaneous PET/MRI

Respiratory and cardiac motion is the most serious limitation to whole-body PET, resulting in spatial resolution close to 1 cm. Furthermore, motion-induced inconsistencies in the attenuation measurements often lead to significant artifacts in the reconstructed images. Gating can remove motion artifacts at the cost of increased noise. This paper presents an approach to respiratory motion correction using simultaneous PET/MRI to demonstrate initial results in phantoms, rabbits, and nonhuman primates and discusses the prospects for clinical application.

METHODS

Studies with a deformable phantom, a free-breathing primate, and rabbits implanted with radioactive beads were performed with simultaneous PET/MRI. Motion fields were estimated from concurrently acquired tagged MR images using 2 B-spline nonrigid image registration methods and incorporated into a PET list-mode ordered-subsets expectation maximization algorithm. Using the measured motion fields to transform both the emission data and the attenuation data, we could use all the coincidence data to reconstruct any phase of the respiratory cycle. We compared the resulting SNR and the channelized Hotelling observer (CHO) detection signal-to-noise ratio (SNR) in the motion-corrected reconstruction with the results obtained from standard gating and uncorrected studies.

RESULTS

Motion correction virtually eliminated motion blur without reducing SNR, yielding images with SNR comparable to those obtained by gating with 5-8 times longer acquisitions in all studies. The CHO study in dynamic phantoms demonstrated a significant improvement (166%-276%) in lesion detection SNR with MRI-based motion correction as compared with gating (P < 0.001). This improvement was 43%-92% for large motion compared with lesion detection without motion correction (P < 0.001). CHO SNR in the rabbit studies confirmed these results.

CONCLUSION

Tagged MRI motion correction in simultaneous PET/MRI significantly improves lesion detection compared with respiratory gating and no motion correction while reducing radiation dose. In vivo primate and rabbit studies confirmed the improvement in PET image quality and provide the rationale for evaluation in simultaneous whole-body PET/MRI clinical studies.

A Markov random field approach for topology-preserving registration: application to object-based tomographic image interpolation

This paper proposes a topology-preserving multiresolution elastic registration method based on a discrete Markov random field of deformations and a block-matching procedure. The method is applied to the object-based interpolation of tomographic slices. For that purpose, the fidelity of a given deformation to the data is established by a block-matching strategy based on intensity- and gradient-related features, the smoothness of the transformation is favored by an appropriate prior on the field, and the deformation is guaranteed to maintain the topology by imposing some hard constraints on the local configurations of the field. The resulting deformation is defined as the maximum a posteriori configuration. Additionally, the relative influence of the fidelity and smoothness terms is weighted by the unsupervised estimation of the field parameters. In order to obtain an unbiased interpolation result, the registration is performed both in the forward and backward directions, and the resulting transformations are combined by using the local information content of the deformation. The method is applied to magnetic resonance and computed tomography acquisitions of the brain and the torso. Quantitative comparisons offer an overall improvement in performance with respect to related works in the literature. Additionally, the application of the interpolation method to cardiac magnetic resonance images has shown that the removal of any of the main components of the algorithm results in a decrease in performance which has proven to be statistically significant.

Spatial Confidence Regions for Quantifying and Visualizing Registration Uncertainty

For image registration to be applicable in a clinical setting, it is important to know the degree of uncertainty in the returned point-correspondences. In this paper, we propose a data-driven method that allows one to visualize and quantify the registration uncertainty through spatially adaptive confidence regions. The method applies to various parametric deformation models and to any choice of the similarity criterion. We adopt the B-spline model and the negative sum of squared differences for concreteness. At the heart of the proposed method is a novel shrinkage-based estimate of the distribution on deformation parameters. We present some empirical evaluations of the method in 2-D using images of the lung and liver, and the method generalizes to 3-D.

Image registration and analysis for quantitative myocardial perfusion: application to dynamic circular cardiac CT

Large area detector computed tomography systems with fast rotating gantries enable volumetric dynamic cardiac perfusion studies. Prospectively, ECG-triggered acquisitions limit the data acquisition to a predefined cardiac phase and thereby reduce x-ray dose and limit motion artefacts. Even in the case of highly accurate prospective triggering and stable heart rate, spatial misalignment of the cardiac volumes acquired and reconstructed per cardiac cycle may occur due to small motion pattern variations from cycle to cycle. These misalignments reduce the accuracy of the quantitative analysis of myocardial perfusion parameters on a per voxel basis. An image-based solution to this problem is elastic 3D image registration of dynamic volume sequences with variable contrast, as it is introduced in this contribution. After circular cone-beam CT reconstruction of cardiac volumes covering large areas of the myocardial tissue, the complete series is aligned with respect to a chosen reference volume. The results of the registration process and the perfusion analysis with and without registration are evaluated quantitatively in this paper. The spatial alignment leads to improved quantification of myocardial perfusion for three different pig data sets.

A cubic B-spline-based hybrid registration of lung CT images for a dynamic airway geometric model with large deformation

The goal of this study is to develop a matching algorithm that can handle large geometric changes in x-ray computed tomography (CT)-derived lung geometry occurring during deep breath maneuvers. These geometric relationships are further utilized to build a dynamic lung airway model for computational fluid dynamics (CFD) studies of pulmonary air flow. The proposed algorithm is based on a cubic B-spline-based hybrid registration framework that incorporates anatomic landmark information with intensity patterns. A sequence of invertible B-splines is composed in a multiresolution framework to ensure local invertibility of the large deformation transformation and a physiologically meaningful similarity measure is adopted to compensate for changes in voxel intensity due to inflation. Registrations are performed using the proposed approach to match six pairs of 3D CT human lung datasets. Results show that the proposed approach has the ability to match the intensity pattern and the anatomical landmarks, and ensure local invertibility for large deformation transformations. Statistical results also show that the proposed hybrid approach yields significantly improved results as compared with approaches using either landmarks or intensity alone.

Accuracy estimation for projection-to-volume targeting during rotational therapy: a feasibility study

PURPOSE

Estimating motion and deformation parameters from a series of projection radiographs acquired during arc therapy using a reference CT volume has become a promising technique for targeting treatment. The purpose of this work is to investigate the influence of rotational arc length on maximum achievable accuracy of motion estimation.

METHODS

The projection-to-volume alignment procedure used a nonrigid model to describe motion in thorax area, a cost function consisting of a least-squared error metric and a simple regularizer that encourages local invertibility, and a four-level multiresolution scheme with a conjugate gradient method to optimize the cost function. The authors tested both small and large scale deformations typically found in the thorax of a radiotherapy patient at different breathing states and limited-angle scans of six angular widths (12 degrees, 18 degrees, 24 degrees, 36 degrees, 60 degrees, and 90 degrees) centered at three angles (0 degrees, 45 degrees, and 90 degrees).

RESULTS

The experiments illustrate the potential accuracy of limited-angle projection-to-volume alignment. Registration accuracy can be sensitive to angular center, tends to be lower along direction of the projection set, and tends to decrease away from the rotation center. The studies of small as well as large but realistically scaled deformations show similar dependencies. These trends appear to have fairly low sensitivity to quantum noise effects.

CONCLUSIONS

There is potentially sufficient information present in a small spread of projections to monitor the configuration of reasonably high contrast tumors without implanted markers.