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Despite reduction in imaging times through improved hardware and rapid acquisition schemes, motion artifacts can compromise image quality in magnetic resonance imaging, especially in three-dimensional imaging with its prolonged scan durations. Direct extension of most state-of-the-art two-dimensional rigid body motion compensation techniques to the three-dimensional case is often challenging or impractical due to a significant increase in sampling requirements. This article introduces a novel motion correction technique that is capable of restoring image quality in motion corrupted two-dimensional and three-dimensional radial acquisitions without a priori assumptions about when motion occurs. The navigating properties of radial acquisitions—corroborated by multiple receiver coils—are exploited to detect actual instances of motion. Pseudorandom projection ordering provides flexibility of reconstructing navigator images from the obtained motion-free variable-width subsets for subsequent estimation of rigid body motion parameters by coregistration. The proposed approach does not require any additional navigators or external motion estimation schemes. The capabilities and limitations of the method are described and demonstrated through simulations and representative volunteer cranial acquisitions. Magn Reson Med 69:1094–1103, 2013. © 2012 Wiley Periodicals, Inc.
Magnetic resonance imaging (MRI) is highly sensitive to patient motion. Depending on the k-space acquisition trajectory, motion can cause blurring, ghosting, or other artifacts that negatively affect image quality , reduce diagnostic information, or require repeated scans. Especially challenging groups include pediatric, uncooperative, and impaired patients. In Cartesian k-space sampling, the approach widely adopted on clinical MRI scanners, patient motion causes significant ghosting artifacts. As prior problems such as gradient and timing instability continue to diminish on new scanners, non-Cartesian trajectories are becoming a more attractive option for providing imaging solutions to these challenging groups. Non-Cartesian trajectories allow for longer data acquisition intervals per pulse repetition time (TR) that allow shorter scans. The variable sampling density of many non-Cartesian scans often allow accelerated imaging through undersampling, especially with time-resolved angiography and dynamic contrast-enhanced (DCE)-MRI . Non-Cartesian sampling plays an important role in many emerging applications including sodium imaging  and ultrashort echo time imaging . Furthermore, non-Cartesian sampling provides a practical platform for acceleration with advanced image reconstruction techniques, such as constrained reconstruction and compressed sensing [5, 6]. For non-Cartesian k-space trajectories, such as radials and spirals [1, 7-9], image artifacts caused by physiological motion (i.e., respiration, cardiac pulsatility, and flow) are more tolerable as they manifest themselves as local blurring . The ability to design a radial projection ordering scheme that provides more uniform k-space coverage further diminishes the effect of data inconsistencies due to motion, producing dispersed streaking artifacts that are much less detrimental for radiological examination than ghosting in Cartesian imaging. These benefits become even more pronounced in three-dimensional (3D) radial imaging where the point spread function is less coherent than for two-dimensional (2D) radial acquisitions. A distinct advantage of radial view ordering is that it samples the center of k-space every TR, thereby obtaining partial or full navigation information that may be useful for motion correction in some applications [7, 10, 11].
Although radial sampling provides some tolerance against physiological motion, bulk motion remains a significant problem, particularly in 3D imaging where prolonged acquisition times increase the likelihood of the occurrence of motion artifacts. Analysis of projection moments in a radial acquisition may provide a way to characterize object motion continuously based solely on the acquired data. Previous work successfully estimated and corrected rigid body translation and rotation using analysis of center of mass (COM) and higher order projection moments , respectively. In theory, these methods apply to both 2D and 3D radial acquisitions; however, 3D implementation is nontrivial due to a large complex search space to correct for rotational motion. Furthermore, the method of translational and rotational motion estimation from projection moments is not robust in the presence of noise, susceptibility artifacts, and trajectory deviations. Finally, as we will demonstrate, analysis of projection moments fails to describe object displacement accurately when imaging with stationary multichannel coils with nonuniform sensitivity profiles, such as those used in parallel MRI.
Alternatively, motion can be tracked with the use of periodically acquired low-resolution navigator images. Many retrospective motion correction techniques [12, 13] rely on assumptions that the object is rigid, and its position and orientation do not change significantly during acquisition of the navigator images. These methods sample central k-space periodically during short segments. Low-resolution images reconstructed from these segments act as navigators for consequent motion correction. One such approach, PROPELLER , has achieved widespread use in clinical applications, particularly in cranial imaging where motion conforms well to a rigid-body model. PROPELLER acquires Cartesian k-space data in successively rotated strips of parallel lines (“blades”). The original 2D PROPELLER approach relies on the assumptions that no motion occurs during the acquisition of each blade and that any occurring rigid body motion happens mostly in-plane. The first assumption is valid for typical implementations that acquire individual 2D blades in approximately 100 ms. The second assumption may be more prone to violation, depending on the anatomy of interest but is common to many 2D motion correction schemes. Parameters for translational and rotational in-plane motion can then be accurately determined by preprocessing and coregistering low-resolution data from fully sampled k-space centers of individual blades. Although the original 2D PROPELLER algorithm may in principle be modified to suit different pulse sequences  and acquisition trajectories including 2D radials , it has notable challenges. In particular, to allow for subvoxel motion estimation, wider blades are desired . In multiecho sequences, it is often problematic to satisfy this design criterion due to the finite number of available echoes in the echo train and requires exploring available tradeoffs between long readouts and related image artifacts . At the same time, increasing the number of readouts per blade also increases the probability of intrablade motion, potentially violating the method's assumptions and compromising its accuracy. These problems may be partially alleviated for 2D imaging through parallel MRI with multiple coil receivers . However, a straightforward extension of PROPELLER to 3D for full rigid body motion correction is significantly complicated by a large increase in data sampling requirements.
In this work, we propose a novel adaptive fully 3D motion correction technique based on the use of a 3D radial sampling scheme and multicoil arrays. This method is designed to overcome challenges of the aforementioned motion correction techniques. We assume that patient motion, such as muscle twitching or adjusting for comfort, occurs in a discontinuous manner alternating with relatively motionless periods. This assumption is consistent with related methods [12, 13] which assume that motion is negligible within the acquisition of a navigator image. We demonstrate that although regular COM analysis does not provide accurate estimates of motion parameters in the presence of nonhomogeneous coil sensitivity profiles of stationary phased arrays, it can be a powerful tool for retrospective detection of not only translational but also rotational motion. Thus, we avoid making a priori assumptions about when motion occurs during a scan. Instead, our method identifies consistent variable-width data subsets based on multicoil COM analysis, which are used as navigators for estimation of rigid body motion parameters through coregistration. The obtained motion parameters are used to correct the data from the various motionless positions before final reconstruction.
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We proposed a novel adaptive technique for retrospective 3D motion correction in multicoil 3D projection imaging. The method derives from two existing motion correction approaches, namely projection moments analysis [7, 10, 11] and correction by means of coregistration of low-resolution image navigators calculated from time-localized subsets of radial data [12, 13, 15, 28, 29]. As we demonstrated (Table 1, Fig. 4), existing techniques may become suboptimal for radial imaging with multicoil receivers with highly varying coil sensitivity profiles. In particular, the accuracy of motion parameter estimation using COM analysis drops significantly for stationary multicoil receiver systems (Table. 1). At the same time, the nontrivial propagation of coil sensitivity information during motion enhances the ability of COM analysis to detect the motion instances, including rotational motion (Fig. 4). In radial acquisitions, each readout samples the central part of k-space that contains a major portion of the image information content. Hence, data inconsistencies due to motion within datasets used to obtain low-resolution navigators may significantly affect the quality of such navigators and subsequently derived motion parameters. Although the use of predefined fixed-subset navigators still results in noticeable improvement of image quality (Fig. 5), its performance is hard to predict and will vary depending on when motion occurs within any given subset.
These shortcomings are eliminated with the proposed technique, which makes no a priori assumptions about when motion will occur. Instead, our method takes advantage of self-navigating properties of radial trajectories to determine consistent subsets of readouts based on actual occurrences of motion as detected by COM analysis. This decouples the process of motion detection from the process of motion estimation, leading to significant improvements in image quality (Figs. 6 and 7). An additional advantage of this adaptive approach stems from the fact that the width of motion-free data subsets is critical for success of coregistration-based motion correction . Our assessment of registration accuracy (results not shown) indicates that motion-free subsets should consist of at least 10% of the total number of projections for accurate subvoxel motion estimation in a 3D acquisition, which is consistent with previously published results for 2D motion correction . As our method relies on learning consistent subsets in an adaptive fashion, it allows for better utilization of motion-corrupted data in cases where motion-free periods exceed the duration of an a priori fixed-width navigator images (Figs. 3 and 5). This is particularly important for 3D imaging, where the need for encoding in an additional spatial dimension skews the tradeoff between spatial and temporal resolution of navigator images, which in turn determine the time scale and sensitivity of the motion correction scheme.
Although resolution appeared to be entirely recovered in our studies, there is a small loss of apparent SNR in the restored images (Fig. 7). This effect is likely due to residual gaps in k-space resulting from rotation corrections and rejected interleaves. Missing data manifest itself in the resulting images in the form of streaking artifacts, thereby increasing the signal in the background. This issue is common to many retrospective motion compensation schemes, but in our method, the impact of gaps is minimized by the use of properly distributed radial interleaves. For example, in an extreme case of rotation, a PROPELLER scan may effectively acquire the same blade twice, leaving a full blade width gap in the k-space data. In a similar case using radial interleaves, narrower gaps (wedges with an arc-angle equal to the angular difference between adjacent interleaves) would be introduced in an isotropic pattern. The smaller gaps in the interleaved case should correspond to less intrusive artifacts, similar to the effects of radial undersampling. An optimized reconstruction incorporating iterative density compensation  or parallel imaging, such as that proposed by Bammer et al. , may reduce streaks caused by the residual gaps in k-space and be more apt for interpolating narrow gaps in k-space. In addition, iterative estimation may provide an efficient way to incorporate now-rejected small subsets of data for improved SNR by applying data weighting schemes  to reduce their relative contribution to the reconstructed image.
The efficiency of the proposed method depends on the accuracy of COM calculations that may be affected by systematic errors caused by trajectory deviations due to gradient delays and eddy currents . In addition to the acquisition-time gradient corrections used here, in vivo trajectory calibration may further improve COM estimates calculated from k-space data. In addition, the temporal fidelity of our method depends on the repetition time of the pulse sequence, number of projections in each interleaf, and noise level (Table 2). Although the time scale for motion correction in our current implementation is higher than that of 2D PROPELLER (300 vs. 100 ms), it provides fully 3D motion correction. The time scale may be reduced by using parallel MRI reconstruction to decrease the number of projections in each interleaf . Improvements in COM estimation may also allow reducing the number of projections used to calculate the COM, thus further refining the time resolution for motion detection and in turn providing more accurate subset delineations.
The proposed method is especially well suited to cranial imaging as typical motion during these exams conforms to our assumptions of rigid body and intermittent motion. As with any global registration-based motion correction technique, rapid continuous and nonrigid motions remain problematic for the proposed method . This is a limitation of the proposed technique, which relies on the assumption that there exist time periods sufficient for acquisition of the navigator images during which position and orientation of the object do not change. One potential way to overcome this limitation is by using temporal interpolation to approximate object positions to correct all data points corrupted by continuous motion. To this end, alternative motion detection schemes based on other types of data consistency checks [36-38], correlation-based techniques [39-41], or external motion detection [42, 43] are the subject of future research.